text:
\section{Introduction}
The quest for a quantum gravity theory (QGT) able to conjugate the two pillars of modern physics, quantum field theory (QFT) and general relativity (GR), has been the object of intense scrutiny for several decades by now. Indeed, while QFT and GR have been proved to describe respectively the interaction of elementary particles and astrophysical objects with extraordinary accuracy, we still need a QGT in order to have predictability in extreme situations, like the very early universe or the interior of black holes.
However such a theory, e.g.~something able to describe the interaction and propagation high-energetic small particles on a quantum spacetime, is still missing.

Nonetheless, in the past decades important advancements towards this aim have been accomplished leading to the construction of remarkable theoretical frameworks such as string theory~\cite{Mukhi:2011zz,Aharony:1999ks,Dienes:1996du}, loop quantum gravity~\cite{Sahlmann:2010zf,Dupuis:2012yw}, causal dynamical triangulations \cite{Loll_2019} or causal set theory~\cite{Wallden:2013kka,Wallden:2010sh,Henson:2006kf}.  In most of these theories, a minimum length appears~\cite{Gross:1987ar,Amati:1988tn,Garay1995},  normally associated with the Planck length $\ell_P \sim 1.6\times 10^{-33}$\,cm (corresponding to the energy scale $M_P \sim 1.22\times 10^{19}$\,GeV). This length is supposed to separate somehow the classical and ``quantum'' regimes of spacetime, a transition that might lead to novel scenarios and possible observable implications.

Unfortunately, the aforementioned theories are not yet able to provide definitive predictions concerning the phenomenology associated to this transition (albeit several proposal in this sense are present in the extant literature). Given this state of affairs, in recent times it has been considered an alternative approach: instead of considering a top-down investigation based on some candidate QGT, one can take a complementary bottom-up procedure based on postulating different kind of modifications of the space-time geometry at mesoscopic regimes, i.e., between the observed scales and the Planck one. Such departures from the standard structure of a classical/continuum spacetime can be on one side related to different quantum gravity scenarios, on the other side they are often amenable to phenomenological testing/constraining, so they can potentially provide important clues about the features that a QGT should have in order to be compatible with present observations at energies below the Planck scale.

A very commonly considered scenario is the one in which some local space-time symmetries, such as Poincar\'e invariance, are modified at very high energies.
In particular, a large body of research has been dedicated to the possible phenomenology associated to departures from local Lorentz invariance, focusing mostly on modifications of the dispersion relations for elementary particles of the form $E^2=p^2+m^2+f(E,p,M_P)$. Most interestingly, using current experiments and observations, several significant constraints can be put on the strength of the above introduced Lorentz violating term $f(E,p,M_P)$ (see e.g.~\cite{Mattingly:2005re,Liberati:2013xla}).

Let us stress here that such dispersion relations can be associated alternatively to broken or deformed local Lorentz invariance.
The first scenario, in which Lorentz symmetry (more precisely the relativity principle at its base) is broken, can be considered by studying for example extensions of the standard model of particle physics including terms allowing for Lorentz invariance violation (LIV)~\cite{Colladay:1998fq,Kostelecky:2008ts,Mattingly:2005re,Liberati:2013xla}. Similar studies can be carried on also in the gravitational sector by introducing a suitable dynamical aether vector field, see e.g.~\cite{Jacobson:2000xp,Horava:2009uw,Liberati:2013xla}. Alternatively, one can contemplate different scenarios in which the relativity principle is preserved but its implementation is deformed in the sense that the action of the boosts generator on momenta is modified, so to leave invariant some form of the aforementioned modified dispersion relation. This approach takes the name of doubly special relativity (DSR)~\cite{AmelinoCamelia:2008qg}.

An important characteristic of DSR theories is that, besides a possible deformation of the dispersion relation, a deformed (non-additive) composition law for momenta is necessary.
While the first ingredient (the dispersion relation) can be even unmodified, i.e., have the same expression of SR~\footnote{This happens in the so-called ``classical basis'' of $\kappa$-Poincaré~\cite{Borowiec2010}}, the last one must be always deformed, being then the crucial difference with respect to SR kinematics.

It was ``a posteriori'' recognized that also in this framework a geometrical interpretation of the deformed symmetries is possible through the introduction of a velocity or momentum dependent spacetime. The most common examples of this kind of geometries are Finsler and Hamilton geometries respectively~\cite{miron2001geometry}, and indeed within these frameworks, the aforementioned departures from standard SR have been considered~\cite{Girelli:2006fw,Amelino-Camelia:2014rga,Letizia:2016lew}~\footnote{Albeit, it is perhaps worth stressing that also LIV scenarios can sometime be described via the same kind of momentum/velocity dependent geometries, see e.g.~\cite{Kostelecky:2011qz,Barcelo:2001cp,Weinfurtner:2006wt,Hasse:2019zqi,Stavrinos:2016xyg}.}.
Similarly, momentum dependent geometries in this DSR framework have also been considered in~\cite{Barcaroli:2016yrl,Barcaroli:2015xda,Barcaroli:2017gvg}.

An open problem common to the above mentioned approaches is related to the apparent impossibility to properly take into account the role of the momenta composition law. Nonetheless, in a parallel stream of research it was shown in~\cite{Carmona:2019fwf} that all the ingredients of a relativistic deformed kinematics (modified dispersion relation and composition law) can be obtained from a maximally symmetric momentum space. In particular,  $\kappa$-Poincaré kinematics can be obtained identifying the isometries (translations and Lorentz isometries) and the squared distance of the metric with the deformed composition law, deformed Lorentz transformations and deformed dispersion relation respectively (the last two facts were previously contemplated in Refs.~\cite{AmelinoCamelia:2011bm,Lobo:2016blj}).

In~\cite{Relancio:2020zok,Relancio:2020rys,Relancio:2020mpa,Pfeifer:2021tas,Relancio:2021asx} the proposal of~\cite{Carmona:2019fwf} was generalized so allowing the metric to describe a curved spacetime, so leading to a geometry in the cotangent bundle depending on all the phase-space variables. This scheme is a generalization of the aforementioned Hamilton structures, the so-called generalized Hamilton spaces~\cite{miron2001geometry}. Given the above progresses, it is nowadays possible to attempt some investigations about the phenomenological and theoretical implications of this framework. Attempts in this direction can for example be found in~\cite{Relancio:2020zok,Relancio:2020rys,Relancio:2020mpa}.

In this sense, it is quite clear that black holes are particularly interesting objects as their evaporation appears to be a first example of mixing of QFT and GR. However, they are also a source of apparent contradiction between these established theories. One of the most noticeable examples is the so-called information loss problem associated to quantum black hole evaporation~\cite{Hawking:1976ra}. In the GR framework, it seems to imply an non-unitary evolution of quantum states, so violating a basic tenet of QFT. On the other hand, requiring  unitarity seems to imply a breakdown of the equivalence principle, the base of GR, at the event horizon of the black hole (see e.g. the so-called firewall paradigm proposed in~\cite{Almheiri:2012rt}). Therefore, it is natural and pressing to further understand black holes in the above discussed alternative scenarios, where Lorentz invariance can be broken or deformed, to see if these issues survive or are resolved somehow.

In the LIV framework, black holes have been considered in~\cite{Dubovsky:2006vk,Barausse:2011pu,Blas:2011ni,Bhattacharyya:2015gwa}, showing that particles with different energies see different horizons.
This is problematic, gievn that his feature can in principle be used to violate the second law of thermodynamics already at the classical level, as well as via particle dependent Hawking radiation (see e.g.~\cite{Dubovsky:2006vk}), hence pointing towards a basic inconsistency of the LIV scenarios. However, there is evidence that the dynamical realization of such violations of the second law might be practically precluded (see e.g.~\cite{Benkel:2018abt}) or that the UV completion of LIV theories could remedy at this problem by introducing further geometrical structure to the black hole, the so-called Universal Horizon~\cite{Blas:2011ni}. The latter appears to fix a universal temperature and restore black hole thermodynamics~\cite{Herrero-Valea:2020fqa} (see however also~\cite{Michel:2015rsa}).

In the DSR context, the temperature of black holes has been explored in~\cite{Gim:2014ira,Gim:2015yxa,Mu:2015qna,Kim:2016qtp,Tao:2016baz,Bezerra:2017hrb,Feng:2017iso,Feng:2018jqf,Shahjalal:2018hid}. The main outcome of these investigations is the realization that the the black hole cannot fully evaporate, so ending in a remnant of finite mass. However, in these scenarios the adopted geometrical setting does not include the composition law associated to the deformed kinematics in a clear way, leaving open the question of the compatibility of black hole thermodynamics with momentum dependent geometrical setups fully accounting for the deformed/doubly special relativistic kinematics.

Fortunately, the aforementioned construction of a cotangent bundle metric can be carried on for a Schwarzschild black hole. In this case, a first remarkable result is that, in spite of the particle-dependent modified dispersion relations, there is still a common horizon for all particles, independently of their energy~\cite{Relancio:2020zok}. However, the usual alternative and equivalent definitions of surface gravity~\cite{Cropp:2013zxi} adopted in GR turn out to not coincide anymore, albeit they can do so in a very particular momentum basis~\cite{Relancio:2021asx}. This opens the question if the laws of black hole mechanics/thermodynamics can be generically extended in this context and in which way.

Following this line of research, in this paper we will hence investigate the first two laws of black hole thermodynamics for a cotangent bundle metric compatible with DSR kinematics. We start by introducing cotangent bundle geometries and recalling some previous results in Sec.~\ref{sec:geometrical_intro}. In Sec.~\ref{sec:zero} and \ref{sec:first} we describe the zero and first laws, respectively, recovering (albeit in a subtle way) the same results of GR. Finally, we discuss the open issue and perspectives in Sec.~\ref{sec:conclusions}.

\section{The cotangent bundle geometries framework for DSR}
\label{sec:geometrical_intro}

Let us start by laying down the basic building blocks for our analysis. We shall start by introducing the main geometrical ingredients in the cotangent bundle, show their connection to DSR, and finally review our main results from previous papers about their generalization to curved spacetimes.

\subsection{Cotangent bundle geometries in a nutshell}

In~\cite{miron2001geometry} a line element in the cotangent bundle is defined as
\begin{equation}
\mathcal{G}\,=\, g_{\mu\nu}(x,k) dx^\mu dx^\nu+g^{\mu\nu}(x,k) \delta k_\mu \delta k_\nu\,,
\label{eq:line_element_ps}
\end{equation}
where
\begin{equation}
\delta k_\mu \,=\, d k_\mu - N_{\nu\mu}(x,k)\,dx^\nu\,,
\end{equation}
being  $N_{\nu\mu}(x,k)$ the nonlinear connection coefficients.

In~\cite{miron2001geometry} it is shown that a horizontal curve is determined by the geodesic motion in spacetime given by
\begin{equation}
\frac{d^2x^\mu}{d\tau^2}+{H^\mu}_{\nu\sigma}(x,k)\frac{dx^\nu}{d\tau}\frac{dx^\sigma}{d\tau}\,=\,0\,,
\label{eq:horizontal_geodesics_curve_definition}
\end{equation}
and the change of momentum obtained from
\begin{equation}
\frac{\delta k_\lambda}{d \tau}\,=\,\frac{dk_\lambda}{d\tau}-N_{\sigma\lambda} (x,k)\frac{dx^\sigma}{d\tau}\,=\,0\,,
\label{eq:horizontal_momenta}
\end{equation}
where
\begin{equation}
{H^\rho}_{\mu\nu}(x,k)\,=\,\frac{1}{2}g^{\rho\sigma}(x,k)\left(\frac{\delta g_{\sigma\nu}(x,k)}{\delta x^\mu} +\frac{\delta g_{\sigma\mu}(x,k)}{\delta  x^\nu} -\frac{\delta g_{\mu\nu}(x,k)}{\delta x^\sigma} \right)\,,
\label{eq:affine_connection_st}
\end{equation}
is the affine connection of spacetime, and
\begin{equation}
\frac{\delta}{\delta x^\mu}\, \doteq \,\frac{\partial}{\partial x^\mu}+N_{\nu\mu}(x,k)\frac{ \partial}{\partial k_\nu}\,.
\label{eq:delta_derivative}
\end{equation}
Here, $\tau$ plays the role of the proper time or the affine parametrization depending if one is considering a massive or a massless particle, respectively.

The choice of the nonlinear connection coefficients $N_{\nu\mu}(x,k)$ is not unique but, as it is shown in~\cite{miron2001geometry}, there is one and only one choice of nonlinear connection coefficients that leads to a space-time affine connection which is metric compatible and torsion free.
When the space-time affine connection is momentum independent, which does not necessarily implies that the momentum metric must also show such behavior,  the coefficients of the nonlinear connection are given by
\begin{equation}
N_{\mu\nu}(x,k)\, = \, k_\rho {\Gamma^\rho}_{\mu\nu}(x)\,,
\label{eq:nonlinear_connection}
\end{equation}
where $ \Gamma^\rho_{\mu\nu}(x)$ is the GR affine connection. From here it is easy to see that,  when the metric does not depend on the space-time coordinates, these coefficients vanish.

In~\cite{miron2001geometry} the covariant derivatives in space-time were defined as
\begin{equation}
\begin{split}
&T^{\alpha_1 \ldots\alpha_r}_{\beta_1\ldots\beta_s;\mu}(x,k)\,=\,\frac{\delta T^{\alpha_1 \ldots\alpha_r}_{\beta_1\ldots\beta_s}(x,k)}{\delta x^\mu}+T^{\lambda \alpha_2 \ldots\alpha_r}_{\beta_1\ldots\beta_s}(x,k){H^{\alpha_1}}_{\lambda \mu}(x,k)+\cdots+\\
&T^{\alpha_1 \ldots \lambda}_{\beta_1\ldots\beta_s}(x,k){H^{\alpha_r}}_{\lambda \mu}(x,k)-T^{\alpha_1 \ldots \alpha_r}_{\lambda \beta_2\ldots\beta_s}(x,k){H^{\lambda}}_{\beta_1 \mu}(x,k)-\cdots-T^{\alpha_1 \ldots \alpha_r}_{\beta_1\ldots \lambda}(x,k){H^{\lambda}}_{\beta_s \mu}(x,k)\,.
\label{eq:cov_dev_st}
\end{split}
\end{equation}
Also, it can be shown~\cite{miron2001geometry} that, given a metric, there is always a symmetric non-linear connection leading to metric compatible affine connections in spacetime so that $g_{\mu\nu;\rho}(x,k)=0$.

In order to study the thermodynamics of black holes, we need to know how the Lie derivative is deformed in this context. In~\cite{Barcaroli:2015xda,Relancio:2020zok} the modified Killing equation for a metric in the cotangent bundle was derived
\begin{equation}
\frac{\partial g_ {\mu\nu}(x,k)}{\partial x^\alpha} \chi^\alpha  -\frac{\partial g_ {\mu\nu}(x,k)}{\partial k_\alpha}\frac{\partial \chi^\gamma}{\partial x^\alpha}k_\gamma + g_{\alpha\nu}(x,k)\frac{\partial\chi^\alpha}{\partial x^\mu}+ g_{\alpha\mu}(x,k)\frac{\partial\chi^\alpha}{\partial x^\nu}\,=\,0\,,
\label{eq:killing}
\end{equation}
where $\chi^\alpha=\chi^\alpha(x)$ is momentum independent. In GR, where the metric does not depend on the momentum, the previous condition can be written as
\begin{equation}
\chi_{\mu\,;\nu}+\chi_{\nu\,;\mu}\,=\,0\,.
\label{eq:killing_GR}
\end{equation}

In~\cite{Relancio:2020zok} it was shown that the Killing equation~\eqref{eq:killing} can be written as (for the particular case in which the affine connection and the nonlinear coefficients are related as in Eq.~\eqref{eq:nonlinear_connection})
\begin{equation}
\chi_{\mu\,;\nu}+\chi_{\nu\,;\mu}-\frac{\partial g_{\mu\nu}}{\partial k_\sigma}\chi^\rho_{;\sigma} k_\rho\,=\,0\,.
\label{eq:killing_DGR}
\end{equation}

\subsection{Deformed relativistic kinematics in curves spacetimes}
We summarize here our previous results about supplementing a deformed relativistic kinematics within a curved spacetime.

The deformed kinematics of DSR are usually obtained from Hopf algebras~\cite{Majid:1995qg}, being the $\kappa$-Poincaré kinematics~\cite{Majid1994}  the most studied example of this kind of construction. This kinematics has been understood from a geometrical point of view in~\cite{Carmona:2019fwf}. Given a de Sitter momentum metric $ \tilde{g}$, translations can be used to define the associative deformed composition law, the Lorentz isometries lead to the Lorentz transformations, and the (squared of the) distance in momentum space is identified with the deformed Casimir.

In~\cite{Relancio:2020zok,Pfeifer:2021tas}, we extended~\cite{Carmona:2019fwf} in order to consider in the same framework a deformed kinematics and a curved spacetime. For that aim, it is mandatory to consider the cotangent bundle geometry above discussed. The metric tensor $g_{\mu\nu}(x,k)$ in the cotangent bundle depending on space-time coordinates was constructed via the space-time tetrad and the metric in momentum space, $\tilde{g}$, so that
\begin{equation}
g_{\mu\nu}(x,k)\,=\,e^\alpha_\mu(x) \tilde{g}_{\alpha\beta}(\bar{k})e^\beta_\nu(x)\,,
\label{eq:definition_metric_cotangent}
\end{equation}
where $\bar{k}_\alpha=\bar{e}^\nu_\alpha (x) k_\nu$, and $\bar{e}$ denotes the inverse of the space-time tetrad.

In~\cite{Relancio:2020rys} it was also proved that this Hamiltonian can be identified with the square of the minimal geometric distance of a momentum $k$ from the origin of momentum space, relating  the Casimir and the metric in the following way~\cite{Relancio:2020zok}
\begin{equation}
\mathcal{C}(x,k)\,=\,\frac{1}{4} \frac{\partial \mathcal{C}(x,k)}{\partial k_\mu} g_{\mu\nu} (x,k) \frac{\partial \mathcal{C}(x,k)}{\partial k_\nu}\,.
\label{eq:casimir_metric}
\end{equation}
It is also possible to choose any function of such Casimir as a new Casimir, which tantamount to make a redefinition of the mass~\cite{Carmona:2019fwf}.

A very important relation satisfied by the Casimir  is that its delta derivative~\eqref{eq:delta_derivative} is zero, i.e.
\begin{equation}
\frac{\delta \mathcal{C}(x,k)}{\delta x^\mu}\,=\,0\,.
\label{eq:casimir_delta}
\end{equation}
This is a necessary condition derived from the fact the Hamilton equations of motions are horizontal curves~\cite{Relancio:2020rys}.

In~\cite{Pfeifer:2021tas} we showed that the most general form of the metric, in which the construction of a deformed kinematics in a curved space-time background is allowed, is a momentum basis whose Lorentz isometries are linear transformations in momenta, i.e., a metric of the form
\begin{equation}
\tilde{g}_{\mu\nu}(k)\,=\,\eta_{\mu \nu} f_1 (k^2)+\frac{k_\mu k_\nu}{\Lambda^2} f_2(k^2)\,,
\label{eq:lorentz_metric}
\end{equation}
where $\Lambda$ is the high-energy scale parametrizing the momentum deformation of the metric and kinematics,  $\eta_{\mu\nu}$ is the Minkowski metric, and $k^2=k_\mu \eta^{\mu\nu}k_\nu$ . It is also important to note that, in order to have a smooth limit to SR,
\begin{equation}
f_1(0)\,=\,1 \,,\qquad f_2(0)\,=\,\text{const}\,.
\label{eq:functions}
\end{equation}

From Eq.~\eqref{eq:definition_metric_cotangent} one obtains the following metric in the cotangent bundle when a curvature in spacetime is present
\begin{equation}
g_{\alpha\beta}(x,k)\,=\,a_{\alpha\beta}(x)f_1 (\bar{k}^2)+\frac{k_\alpha k_\beta}{\Lambda^2} f_2(\bar{k}^2)\,,
\label{eq:lorentz_metric_curved}
\end{equation}
where $a_{\mu \nu}(x) = e^\alpha_\mu(x) \eta_{\alpha\beta} e^\beta_\nu(x)$ is the GR metric, and $\bar k^2=\bar k_\mu \eta^{\mu\nu} \bar k_\nu=k_\mu a^{\mu\nu}(x)  k_\nu$. Therefore, one can use the definition of the space-time affine connection~\eqref{eq:affine_connection_st} to show that this connection is momentum independent, being then $ H^\rho_{\mu\nu}(x,k)=\Gamma^\rho_{\mu\nu}(x)$, the same one of GR~\cite{Pfeifer:2021tas}.

Since we want the momentum metric~\eqref{eq:lorentz_metric} to be a de Sitter space (allowing us to define a deformed relativistic kinematics), a relationship between the functions $f_1$ and $f_2$ must hold. In particular, in~\cite{Relancio:2020rys} it was shown that, in order to be conserved the Einstein's tensor, as defined in~\cite{miron2001geometry} (which is the same expression of GR), the metric~\eqref{eq:lorentz_metric_curved} must be conformally flat. Then, taking $f_2=0$ and imposing a momentum de Sitter space, one obtains from Eq.~\eqref{eq:lorentz_metric_curved}
\begin{equation}
g_{\mu\nu}(x,k)\,=\,a_{\mu \nu}(x)\left(1-\frac{\bar{k}^2}{4\Lambda^2}\right)^2\,.
\label{eq:conformal_metric}
\end{equation}

\subsection{Black holes in the cotangent bundle}
\label{subsec:BH}

Following the above definitions, it is easy to see that the deformed Kerr metric in the Boyer-Lindquist coordinates reads
 \begin{equation}
 \begin{split}
ds^2\,=\,& f_1(\bar k^2)\left(-\left(1-\frac{2 M  r}{\rho^2}\right) d v^2+2 d v\,d r-2 a \sin^2  \theta \, d r\, d\psi -\frac{4 M a  r \sin^2  \theta }{\rho^2} d v \, d \psi \right.\\
&\left. +\frac{\Sigma }{\rho^2} \sin^2  \theta\,  d\psi^2 +\rho^2 d \theta^2\right) +\frac{f_2(\bar k^2)}{\Lambda^2}\left(k_v dv +k_r dr+k_\theta d\theta+k_\psi d\psi \right)^2 \,,
 \end{split}
\label{eq:line_kerr}
\end{equation}
where
\begin{equation}
\Sigma\,=\, \left( r^2+a^2\right)^2-a^2 \Delta  \sin^2  \theta\,,\qquad \Delta\,=\,  r^2-2M  r-a^2\,,\qquad \rho^2\,=\,  r^2+a^2  \cos^2  \theta\,.
\end{equation}

In~\cite{Relancio:2021asx} it was found that only for the basis leading to Eq.~\eqref{eq:conformal_metric} the diverse possible notions of surface gravity coincide. While this is always true in GR when there is a Killing horizon~\cite{Cropp:2013zxi}, this is not longer true in these generic cotangent bundle manifolds. However, for the basis of Eq.~\eqref{eq:conformal_metric}, in contrast with any other momentum coordinates, the Killing equation can be written as in GR, i.e., Eq.~\eqref{eq:killing_GR}, allowing for the usual derivation of surface gravity definition to go trough.

In spite of this, we shall try to keep our analysis as general as possible, and hence, in what follows, we will use the general form Eq.~\eqref{eq:lorentz_metric_curved}, with generic functions $f_1$ and $f_2$.

\section{Zero law}
\label{sec:zero}
As we saw in~\cite{Relancio:2021asx}, the surface gravity obtained from the inaffinity of null geodesics is the same of the one of GR for a generic metric of the form of~\eqref{eq:lorentz_metric_curved}, i.e., independently of the choice of $f_1$ and $f_2$. Here we show that, for any choice of these functions, the surface gravity is a constant, as in GR, when considering massless particles.  For that aim, we start by showing that the Killing energy is still a conserved quantity. From the aforementioned definition of the surface gravity we are able to prove that the
 ``generator'' surface gravity~\cite{Cropp:2013zxi}, another common (and useful) notion, is the same one of GR, and hence coincides with $\kappa_\text{inaffinity}$, independently again on the functions $f_1$ and $f_2$. Given that, it is easy to prove that the zero law is still valid in this scheme.

\subsection{Conserved Killing energy}

We start by considering the derivative of the Killing energy with respect the affine parameter $\tau$
 \begin{equation}
 \frac{d (u^\alpha \chi_\alpha)}{d\tau}\,=\,  \left(u^\alpha \chi_\alpha\right)_{;\mu} u^\mu\,,
\label{eq:killing_energy}
\end{equation}
where $u^\alpha$ is the velocity vector. As showed in~\cite{Relancio:2020rys}, the derivative with respect to $\tau$ can be expressed also in this cotangent bundle framework as a covariant derivative contracted with the velocity. For our case study we will consider only massless particles, so $u^2=0$. This also means that, due to the linear Lorentz covariant form of the metric~\eqref{eq:lorentz_metric_curved}, the same relation between momentum and velocity of GR holds in this scheme ($k_\mu=a_{\mu\nu}u^\nu$), and therefore
 \begin{equation}
k_\mu g^{\mu\nu} k_\nu\,=\,k_\mu a^{\mu\nu} k_\nu\,=\,k_\mu u^\mu\,=\,0\,,
\label{eq:v_k_null}
\end{equation}
since $\bar k^2 =0$.

We can now expand Eq.~\eqref{eq:killing_energy} as
\begin{equation}
u^\alpha_{;\mu} u^\mu \chi_\alpha+u^\alpha u^\mu \chi_{\alpha;\mu}\,=\, \frac{1}{2}\frac{\partial g_{\mu\alpha}}{\partial k_\sigma}\chi^\rho_{;\sigma} k_\rho  u^\alpha u^\mu \,=\, - g_{\mu\alpha}\frac{\partial  u^\alpha}{\partial k_\sigma}  u^\mu  {\chi^\rho}_{;\sigma} k_\rho\,=\,0\,,
\label{eq:killing_energy2}
\end{equation}
where in the second step we have used the geodesic equation and the Killing equation~\eqref{eq:killing_DGR}, in the third one the fact that $u^2=0$, and in the last one the fact that the four-velocity for massless particles does not depend on $k$, since  they probe a momentum independent geometry as it can be seen by contracting~\eqref{eq:lorentz_metric_curved} twice with the momentum $k^\mu$. With this we show that, for massless particles, there is a conserved quantity along a geodesic, which is the usual Killing energy, and that the following relation holds
 \begin{equation}
 u^\alpha u^\mu \chi_{\alpha;\mu}\,=\,0\,,
\label{eq:killing_vector_v}
\end{equation}
which will be useful in the following.

\subsection{Generator surface gravity}
It was shown in~\cite{Relancio:2021asx} that the surface gravity, defined as the inaffinity of the generators of the horizon, is the same as in GR for a black hole metric of the from~\eqref{eq:lorentz_metric_curved}, i.e.
 \begin{equation}
 \chi^\nu\,  {\chi^\mu}_{;\nu} \,=\,\kappa_{\text{inaffinity}} \chi^\mu\,.
\label{eq:inaffinity}
\end{equation}
This is due to the fact that, if the  Killing vector is a constant in the GR metric, it will be still constant also in our framework. This can be understood just by looking at Eq.~\eqref{eq:killing}. Therefore, the surface gravity defined in Eq.~\eqref{eq:inaffinity} will be the same one of GR, since the affine connection is also momentum independent.

We now follow the procedure given in~\cite{Wald:1984rg}, using the Frobenius' theorem~\cite{Poisson:2009pwt}, which states that if a congruence of geodesics has a vanishing rotation tensor, the Killing vector field $\chi_\alpha$ satisfies
 \begin{equation}
 \chi_{[\alpha;\beta} \chi_{\gamma]}\,=\,0\,,
\label{eq:frobenius}
\end{equation}
where the brackets denote indexes antisymmetrization.  Using the Killing equation~\eqref{eq:killing_DGR} we can write the previous expression as
 \begin{equation}
 2 \left( \chi_{\alpha;\beta}\chi_\gamma +\chi_{\gamma;\alpha}\chi_\beta +\chi_{\beta;\gamma}\chi_\alpha \right)\,=\, {\chi^\epsilon}_{;\delta}k_\epsilon\left( \frac{\partial g_{\alpha\beta}}{\partial k_\delta} \chi_\gamma+ \frac{\partial g_{\alpha\gamma}}{\partial k_\delta}  \chi_\beta+ \frac{\partial g_{\beta\gamma}}{\partial k_\delta} \chi_\alpha\right)\,.
\label{eq:frobenius2}
\end{equation}
Multiplying the previous equation by $\chi^{\alpha;\beta}$ we find
 \begin{equation}
 2 \left( \chi_{\alpha;\beta}\chi^{\alpha;\beta}\chi_\gamma+2\kappa^2\chi_\gamma \right)\,=\, {\chi^\epsilon}_{;\delta}k_\epsilon\left( \frac{\partial g_{\alpha\beta}}{\partial k_\delta} \chi_\gamma \chi^{\alpha;\beta}+ 2\kappa \frac{\partial g_{\alpha\gamma}}{\partial k_\delta}  \chi^\alpha  \right)\,,
\label{eq:frobenius3}
\end{equation}
where we have used again~\eqref{eq:killing_DGR}. In order to find a simple relation between the surface gravity and the Killing vector, we can see the explicit form of the derivative of the metric~\eqref{eq:lorentz_metric_curved} with respect the momentum
 \begin{equation}
\frac{\partial g_{\alpha\beta}}{\partial k_\delta}\,=\, 2 \frac{k_\rho a^{\rho\delta}}{\Lambda^2} \left(a_{\alpha\beta}\frac{\partial f_1}{\partial \bar k^2}+\frac{k_\alpha k_\beta}{\Lambda^2}\frac{\partial f_2}{\partial \bar k^2}\right)+\frac{f_2}{\Lambda^2}\left(k_\alpha \delta^\delta_\beta+k_\beta \delta^\delta_\alpha\right)\,.
\label{eq:dg_dk}
\end{equation}
Using Eq.~\eqref{eq:killing_vector_v} we can see that, when substituting the previous equation into Eq.~\eqref{eq:frobenius3}, the first term of Eq.~\eqref{eq:dg_dk} vanishes. Therefore, we focus on the terms of the right hand side of Eq.~\eqref{eq:frobenius3} when substituting the second term of~\eqref{eq:dg_dk}. Indeed we find
 \begin{equation}
\begin{split}
{\chi^\epsilon}_{;\delta} k_\epsilon &\left( \frac{\partial g_{\alpha\beta}}{\partial k_\delta} \chi_\gamma \chi^{\alpha;\beta}+ 2\kappa \frac{\partial g_{\alpha\gamma}}{\partial k_\delta}  \chi^\alpha  \right)\,=\,k_\epsilon \frac{f_2}{\Lambda^2}\left(k_\alpha \chi_\gamma {\chi^\epsilon}_{;\delta}  \left( \chi^{\alpha;\delta}+ \chi^{\delta;\alpha}\right)\right. \\ &\left.+2 \kappa \left(k_\gamma  \chi^\delta {\chi^\epsilon}_{;\delta}  +k_\alpha \chi^\alpha {\chi^\epsilon}_{;\gamma}  \right)\right)
\,=\,k_\epsilon \frac{f_2}{\Lambda^2}\left(k_\alpha \chi_\gamma {\chi^\epsilon}_{;\delta}  \frac{\partial g^{\alpha \delta}}{k_\rho} {\chi^{\sigma}}_{;\rho}k_\sigma\right.\\
&\left.+2 \kappa \left(k_\gamma \kappa \chi^\epsilon +k_\alpha \chi^\alpha {\chi^\epsilon}_{;\gamma}  \right)\right)\,=\, 2\kappa\frac{f_2}{\Lambda^2}    k_\epsilon\left(k_\gamma \kappa \chi^\epsilon +k_\alpha \chi^\alpha {\chi^\epsilon}_{;\gamma}  \right) \,,
\label{eq:frobenius4}
\end{split}
\end{equation}
where we have used  Eqs.~\eqref{eq:killing_DGR} and \eqref{eq:inaffinity}, and in the last one Eq.~\eqref{eq:killing_vector_v}.
Hence, we can now write Eq.~\eqref{eq:frobenius3} as
 \begin{equation}
 2 \left( \chi_{\alpha;\beta}\chi^{\alpha;\beta}\chi_\gamma+2\kappa^2\chi_\gamma \right)\,=\, 2\kappa\frac{f_2}{\Lambda^2}    k_\epsilon\left(k_\gamma \kappa \chi^\epsilon +k_\alpha \chi^\alpha {\chi^\epsilon}_{;\gamma}   \right)\,.
\label{eq:frobenius5}
\end{equation}
When multiplying the previous equation by $k^\gamma$ we find that the right hand side vanishes by virtue of Eqs.~\eqref{eq:v_k_null} and \eqref{eq:killing_vector_v}, so we recover
 \begin{equation}
 \kappa^2 \,=\,- \frac{1}{2}  \chi_{\alpha;\beta}\chi^{\alpha;\beta} \,.
\label{eq:frobenius_gr}
\end{equation}
In conclusion, we have proved that for a generic metric of the form~\eqref{eq:lorentz_metric_curved}, the surface gravity defined from the horizon's null generators, can be written as in GR.

Actually, we can also show that this is the very same expression of GR. We start by writing the inverse of the metric~\eqref{eq:lorentz_metric_curved}
\begin{equation}
g^{\alpha\beta}(x,k)\,=\,a^{\alpha\beta}(x)\frac{1}{f_1 (\bar{k}^2)}-a^{\delta\alpha}(x) a^{\gamma\beta}(x) k_\delta k_\gamma\frac{ f_2(\bar{k}^2)}{ f_1(\bar{k}^2)\left( f_1(\bar{k}^2) \Lambda^2 + f_2(\bar{k}^2)\bar{k}^2\right)}\,.
\label{eq:lorentz_metric_curved_inv}
\end{equation}
Now we can use the metric~\eqref{eq:lorentz_metric_curved} and its inverse~\eqref{eq:lorentz_metric_curved_inv} to rewrite the right hand side of Eq.~\eqref{eq:frobenius_gr} as
 \begin{equation}
 \begin{split}
 {\chi^\alpha}_{;\beta}{\chi^\gamma}_{;\delta}g_{\alpha\gamma}&g^{\beta\delta}\,=\,  {\chi^\alpha}_{;\beta}{\chi^\gamma}_{;\delta}\left(a_{\alpha\gamma}a^{\delta\beta}+\frac{f_2}{f_1\Lambda^2}k_\alpha k_\gamma a^{\beta\delta}\right.\\
 &\left.-a_{\alpha\gamma} a^{\delta\sigma}  a^{\rho\beta} k_\sigma k_\rho\frac{ f_2 }{ f_1  \Lambda^2 + f_2 \bar{k}^2}- a^{\delta\sigma}  a^{\rho\beta} k_\sigma k_\rho k_\alpha k_\gamma \frac{ f_2^2 }{f_1\left( f_1  \Lambda^2 + f_2 \bar{k}^2\right)}\right) \,.
\label{eq:frobenius_gr2}
 \end{split}
\end{equation}
The last term vanishes by virtue of Eq.~\eqref{eq:killing_vector_v}. Moreover, when considering massless particles, $\bar k^2=0$, so the coefficients of the second and third terms are the same. By taking into account Eq.~\eqref{eq:killing_GR}, which is valid for the GR metric $a_{\mu \nu}$, one can finally obtain
 \begin{equation}
 \kappa^2 \,=\,- \frac{1}{2}   {\chi^\alpha}_{;\beta}{\chi^\gamma}_{;\delta}a_{\alpha\gamma}a^{\beta\delta} \,,
\label{eq:frobenius_gr3}
\end{equation}
which is exactly the same momentum independent GR expression, which we already know to be equivalent to $\kappa_\text{inaffinity}$.

\subsection{Uniformity of the surface gravity on the horizon}
Strong of the above results, it is now trivial to prove that the surface gravity is uniform on the event horizon even in our cotangent bundle setting. Since we have seen that the surface gravity defined from null generators~\eqref{eq:frobenius_gr3} is momentum independent, we can follow the usual GR procedure. As showed in~\cite{Wald:1984rg}, from Eq.~\eqref{eq:killing_GR} one can obtain
 \begin{equation}
{\chi^\alpha}_{;\mu;\nu} \,=\,{R^\alpha}_{\mu\nu\sigma}(x)\chi^\sigma \,,
\label{eq:2cov_dev}
\end{equation}
where ${R^\sigma}_{\alpha\mu\nu}(x)$ is the Riemann's tensor~\footnote{Note that, while in a generic cotangent bundle metric the Riemann tensor, defined from the commutator of two covariant derivatives, depends also on the momentum, this is not the case for our particular metric~\eqref{eq:lorentz_metric_curved}, since the affine connection is the same one of GR. Moreover, since the Killing vector is momentum independent, there are not extra (momentum dependent) terms that should be taken into account in~\eqref{eq:2cov_dev}~\cite{miron2001geometry}}. Using this expression, we can see from Eq.~\eqref{eq:frobenius_gr3}
 \begin{equation}
 \chi^{\sigma}\kappa^2_{;\sigma} \,=\, 2 \kappa \chi^{\sigma}\kappa_{;\sigma} \,=\,-  {\chi^\alpha}_{;\beta}a_{\alpha\gamma}a^{\beta\delta} {R^\gamma}_{\delta\rho\sigma}\chi^\rho \chi^{\sigma}\,=\,0\,,
\label{eq:kappa_der1}
\end{equation}
due to the symmetry of the Riemann's tensor. Similarly one can also prove that along a transverse direction the surface gravity is a conserved quantity, as in~\cite{Wald:1984rg}.

Therefore, in this section we have proved that the zero law of black hole thermodynamics is also valid in this scheme, independently of the choice of the function $f_1$ and $f_2$ defining the momentum metric.

\section{  Smarr's formula and first law}
\label{sec:first}
In this section we discuss the Smarr's formula and the first law of black hole thermodynamics, which can be derived from the former. In particular we show that, by taking into account that the physical distance measured by the particle {probing the spacetime} is momentum dependent, one finds no modification with respect to the GR scenario.

\subsection{Smarr's formula}
We start by regarding the space-time line element from Eq.~\eqref{eq:line_element_ps}, which is
  \begin{equation}
ds^2\,=\, dx^\mu g_{\mu\nu}(x,k)dx^\nu\,.
\label{eq:line_element_st}
\end{equation}
In order to take into account the momentum dependent effects when regarding this line element, we must substitute momenta as a function of the space-time coordinates~\footnote{Through a space-time geodesic (horizontal curve) momenta satisfy Eq.~\eqref{eq:horizontal_momenta}, being then a function of the velocity and the space-time coordinates. In particular, there is a very simple way to find this dependence: since the velocity can be obtained as a function of the coordinates by solving the geodesic equation~\eqref{eq:horizontal_geodesics_curve_definition} (remember that in our framework the space-time affine connection is momentum independent), momenta can be written as the same function times the GR metric, due to the fact that in this scenario, $k_\mu =a_{\mu \nu}(x)v^\nu$ for massless particles.}. Therefore, the line element becomes
  \begin{equation}
ds^2\,=\, dx^\mu g_{\mu\nu}(x,k(x))dx^\nu\,.
\label{eq:line_element_st2}
\end{equation}
Since we are interested in this section in computing the area as an integral, using the space-time line element, we can define new  effective space-time coordinates, $\tilde x^\mu$~\cite{Relancio:2020mpa}, in such a way that the previous line element can be written as
  \begin{equation}
ds^2\,=\, d\tilde{x}^\mu a_{\mu\nu}(\tilde{x})d\tilde{x}^\nu\,,
\label{eq:line_element_st_t}
\end{equation}
which is the same line element of GR but in these new tilde coordinates. In this way we are assuming that the physical distance traveled by a particle, through a momentum dependent geometry, is also momentum dependent.

Note that this change of variables cannot be made in general since the metric is not invariant under change of momentum coordinates~\cite{Relancio:2020rys}. However, since we are only interested in the measure on spacetime, we can freely use this definition. In particular, if the momentum metric can be written as a function of a tetrad,
\begin{equation}
    \tilde g_{\mu\nu}(\bar k)\,=\,\varphi^\alpha_\mu(\bar k) \eta_{\alpha\beta} \varphi^\beta_\nu(\bar k)\,,
\end{equation}
the new tilde coordinates can be expressed through the following relationship
\begin{equation}
    d  \tilde x^\mu e^\alpha_\mu (\tilde x)\,=\,   d x^\mu e^\beta_\mu (x)\varphi^\alpha_\beta(\bar k)\,.
\end{equation}

This allows us to rederive the Smarr's formula in a simple and direct way. We start by considering the area of the horizon of a black hole.  We use the following coordinates of the Kerr's black hole~\cite{Poisson:2009pwt}
 \begin{equation}
 \begin{split}
ds^2\,=\,& -\left(1-\frac{2 M \tilde r}{\tilde\rho^2}\right) d\tilde v^2+2 d\tilde v\,d\tilde r-2 a \sin^2  \tilde\theta \, d\tilde r\, d\tilde\psi -\frac{4 M a \tilde r \sin^2  \tilde\theta }{\tilde\rho^2} d\tilde v \, d\tilde \psi \\
&+\frac{\tilde\Sigma }{\tilde\rho^2} \sin^2 \tilde \theta\,  d\psi^2 +\rho^2 d\tilde \theta^2\,,
\label{eq:line_kerr_tilde}
 \end{split}
\end{equation}
where,
 \begin{equation}
\tilde\Sigma\,=\, \left(\tilde r^2+a^2\right)^2-a^2 \tilde\Delta  \sin^2 \tilde \theta\,,\qquad \tilde\Delta\,=\, \tilde r^2-2M \tilde r-a^2\,,\qquad \tilde\rho^2\,=\, \tilde r^2+a^2  \cos^2  \tilde\theta\,.
\end{equation}
The area is defined as
 \begin{equation}
A\,=\, \oint_\mathcal{H} \sqrt{\tilde\sigma} d^2\tilde\theta \,,
\label{eq:area}
\end{equation}
 where $\mathcal{H}$ is a two-dimensional cross section of the event horizon, for $\tilde v$ constant, $\tilde r=\tilde r_+=r_+=M+\sqrt{M^2-a^2}$, $0\leq\tilde \theta\leq \pi$, and  $0\leq\tilde\psi<2\pi$. The equality $\tilde r_+= r_+$ holds because the event horizon is the same for all massless particles, independently of their energy~\cite{Relancio:2020zok}. This can be easily understood from the fact that the geodesics of massless particles are undeformed for the metric~\eqref{eq:lorentz_metric_curved}, as explained previously.

Using~\eqref{eq:line_kerr_tilde} one  finds
 \begin{equation}
\sqrt{\tilde\sigma}\,=\, \sqrt{  \tilde\Sigma \sin^2 \tilde \theta } \,,
\end{equation}
so one obtains from Eq.~\eqref{eq:area}
 \begin{equation}
A\,=\, 4 \pi\left(r_+^2+a^2\right)\,.
\label{eq:area2}
\end{equation}
In order to derive the Smarr's formula we start by multiplying the area by the surface gravity $\kappa=\sqrt{M^2-a^2}/\left(r_+^2+a^2\right)$~\footnote{Remember that in the previous section we have shown that the same GR surface gravity is also obtained in this cotangent bundle framework from the inaffinity and generator definition.}, and dividing it by $4\pi$, obtaining
 \begin{equation}
\frac{\kappa A}{4 \pi}\,=\, \left(r_+^2+a^2\right)\frac{\sqrt{M^2-a^2}}{r_+^2+a^2}\,=\, \sqrt{M^2-a^2}\,.
\label{eq:smarr1}
\end{equation}
Now, we can multiply  the angular velocity of the black hole, which is  $\Omega_H=a/(r_+^2+a^2)$, by  $J=M a$, the angular momentum of the black hole, finding the following expression
 \begin{equation}
2 \Omega J\,=\, \frac{2 a^2 M}{r_+^2+a^2}\,.
\label{eq:smarr2}
\end{equation}
Adding Eqs.~\eqref{eq:smarr1} and~\eqref{eq:smarr2}, and using that the explicit value of the event horizon radius, $r_+=M+\sqrt{M^2-a^2}$, one can finally obtain the well-known result
 \begin{equation}
M\,=\, 2 \Omega_H J+\frac{\kappa A}{4 \pi}\,,
\label{eq:smarr}
\end{equation}
which is the same GR expression of the Smarr's formula.

\subsection{First law}
From Eq.~\eqref{eq:smarr} one is able to derive the first law of black hole thermodynamics~\cite{Poisson:2009pwt}. Let us consider a black hole with mass $M$ and angular momentum $J$ that is perturbed, so these parameters become $M+\delta M$ and $J+\delta J$.  We can see that both variations are related by deriving Eq.~\eqref{eq:area2}
 \begin{equation}
\frac{\delta A}{8 \pi}\,=\,  r_+ \delta r_+ + a \delta a\,.
\label{eq:variation_area}
\end{equation}
By taking into account the relationship between $r_+$ and the mass and spin of the black hole we find
 \begin{equation}
\left(r_+-M\right) \delta r_+\,=\,  r_+  \delta M- a \delta a\,,
\label{eq:variation_area2}
\end{equation}
and from here it is easy to verify that
 \begin{equation}
\frac{\kappa}{8 \pi} \delta A \,=\, \delta M- \Omega_H \delta J\,,
\label{eq:variation_area3}
\end{equation}
holds, exactly as in GR.

\section{Conclusion}
\label{sec:conclusions}
In this paper we have addressed, for the first time, the first two black hole laws of thermodynamics in a cotangent bundle geometry associated to the deformed kinematics of doubly special relativity. We have found that these laws are unmodified with respect to the general relativistic setting for the most general metric in the cotangent bundle compatible with a consistent lift of the deformed symmetries on curved spacetimes, Eq.~\eqref{eq:lorentz_metric_curved}.

The zeroth law implies the conservation of the surface gravity, being it a constant for an stationary black hole. In a previous work~\cite{Relancio:2021asx} we have seen that not every notion of surface gravity is equivalent in this scheme, being all of them equal for a particular choice of the momentum metric Eq.~\eqref{eq:conformal_metric}. Combining the results of that paper with the ones presented here, we see that both notions related to inaffinity of geodesics, peeling of null geodesics, and generator of null horizon, coincide for any metric of the form Eq.~\eqref{eq:lorentz_metric_curved}, being them the same one of general relativity. These definitions seems to be more fundamental in our framework as they are valid and equivalent even for the most general metric~\eqref{eq:lorentz_metric_curved}, while the other definitions only agree for the metric displayed in~\eqref{eq:conformal_metric}.

Regarding the first law, we have seen that, taking into account that the physical distance measured by particles is momentum dependent, it leads also to the same result of general relativity. This implies that the same relationship between mass, angular momentum, and area of a black hole, is independent on the particle probing spacetime.

The extension of the remaining two laws of black hole mechanics is far from trivial given that the second law would require a more detailed understanding of the field equations, while the third one would require an in dept analysis of trapped surfaces in our framework. Let us also stress that the recovery of these two laws of black hole mechanics in their usual GR form strongly suggests that the surface gravity will determine the quantum black hole temperature in our framework, as in the usual case. However, a confirmation of this conjecture can only be achieved by a suitable extension of the standard derivation of Hawking radiation based on QFT in curved spacetime to the full cotangent bundle geometry.
We hope to be able to address these open issues in future works.

\section*{Acknowledgments}

JJR acknowledges support from the INFN Iniziativa Specifica GeoSymQFT. SL acknowledge funding from the Italian Ministry of Education and Scientific Research (MIUR) under the grant PRIN MIUR 2017-MB8AEZ. We thank Christian Pfeifer for useful comments.  The authors would also like to thank support from the COST Action CA18108.

redpajama_set_name: RedPajamaArXiv


text:
Biggest deals of 2020: Top office leases in Dallas-Fort Worth
Harwood News
By Ryan Salchert / January 4, 2021 / Dallas Business Journal
As we look back on 2020, the Business Journal compiled a list of the top 10 largest office leases that were signed in Dallas-Fort Worth last year.
This list is based off previous reporting and includes nearly 1.7 million square feet of office space. It is worth noting that this list is based off leases that were signed in 2020 — not when companies actually moved into these new spaces. This list also includes lease renewals:
10. Bell – 109,187-SF
At the beginning of December, it was announced that Fort Worth-based Bell, a Textron Inc. (NYSE: TXT) company and aerospace manufacturer, would be moving into a four-story building previously occupied by American Airlines Federal Credit Union. The company's new address, 4151 Amon Carter Blvd., is part of the larger campus that formerly housed American Airlines' headquarters. The company's new space will house 600 employees.
Transwestern's Duane Henley and Nathan Durham represented the landlord, Austin-based Capital Commercial Investments, while Todd Burnette and Matt Montague with JLL represented Bell Textron in the transaction.
9. The Michaels Cos. Inc. – 123,740-SF
Home goods retailer Michaels is one of two companies on this list to have made a headquarters move within Las Colinas. The Business Journal broke news of Michaels move in July to 3939 W. John Carpenter Freeway, also known as Royal Ridge III. The building had recently been vacated by American Airlines and offered Michaels a plug-and-play opportunity. Michaels new address is less than two miles away from its previous headquarters at 8000 Bent Branch Drive.
JLL's John Brownlee and Michael Williams represented the landlord while Jamie Jennings of Stream Realty Partners and Damian Rivera of ESRP represented Michaels.
8. Haynes and Boone – 125,000-SF
In August, Harwood International announced plans for its newest office building in Uptown, Harwood No. 14. Anchoring the 27-story, 360,000-square-foot building will be Dallas's largest law firm Haynes and Boone LLP. The company plans to take 125,000 square feet at the building by late 2023. The company's current headquarters is at One Victory Park.
Andy Leatherman, Brooke Armstrong, and Brad Selner of JLL represented the tenant while John Lee, Hannah Waidmann and Kelly Whaley of Harwood International represented the landlord.
7. Hilltop Securities – 130,756-SF
Hilltop Securities, a subsidiary of financial holding company Hilltop Holdings (NYSE: HTH), signed a new lease over the summer to relocate its headquarters within downtown Dallas from Renaissance Tower to 717 N. Harwood. The company's new lease will cover multiple floors.
6. Varsity Brands – 135,888-SF
The largest office renewal in 2020 came courtesy of Varsity Brands, which will keep its headquarters at 14460 Varsity Brands Way in Farmers Branch. The company originally bought the building about three years ago and soon after moved its executive team and more than 800 employees there. The lease was the largest of the second quarter, according to reports from Transwestern and CBRE.
5. Southwestern Health Resources – 150,000-SF
Just before Christmas, Southwestern Health Resources revealed it would be moving its headquarters from Dallas to Farmers Branch. The organization leased about 150,000 square feet at 1601 LBJ Freeway, also known as Browning Place I. About 900 employees will work out of the new headquarters, a spokesperson for Southwestern Health Resoruces said. The move is expected to be made in early 2021.
Southwestern Health was previously headquartered at 8150 Brookriver Drive near the Dallas Medical Center. Transwestern's Duane Henley represented the landlord in the deal, while JLL's Paul Whitman represented the tenant.
4. Trinity Industries – 155,185-SF
In April, the Business Journal broke the news that Trinity Industries Inc. (NYSE: TRN) would move its headquarters from 2525 N. Stemmons Freeway to International Plaza II in Far North Dallas. The move is expected to be made in early 2021. The company signed a 16-year lease and will be the anchor tenant at the property.
3. Caliber Home Loans – 159,320-SF
The largest lease of the third quarter came courtesy of Caliber Home Loans, which took nearly 160,000 square feet at 2401 Olympus Blvd. in Cypress Waters. The property was completed earlier in 2020 by Billingsley Co.
2. Oncor Electric Delivery – 200,000-SF
At the beginning of 2020, Dallas-based Oncor Electric Delivery Co. signed a new lease within Fort Worth at 777 Main St. The company will take nearly 200,000 square feet at Fort Worth's third tallest building and will be moving some 600 employees from its former home at 115 West 7th St., also in downtown Fort Worth.
1. Vistra – 403,150-SF
The largest lease of 2020 was revealed in July when a spokesperson for energy company Vistra (NYSE: VST) confirmed the company's new lease at a long-vacant office building in Las Colinas. The Fortune 500 company, which is headquartered in Las Colinas, will be taking more than 400,000 square feet at 1925 W. John Carpenter Freeway, the former home of Bank of America. The building will house Vistra's call center and other operations while its headquarters will remain at 6555 Sierra Drive.

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text:
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Our Lady of Mercy Academy, Newfield dedicated its first school soccer/lacrosse field on Sunday, Nov.r 8. Before guests and friends of the school, Father Paul Galetto, president of St. Augustine Prep, gave a blessing for the student-athletes, officials and coaches. Called Freshwave Field, and named in memory of Anthony and Barbara Consalo, the field also has a scoreboard/sign showing the names of its donors. Above, Michelle McGrath, athletic director, speaks during the ceremony.


text:
Q: Disable archiving support in org-mode in emacs I am hitting the wrong key by mistake in Emacs all the time. This is archiving some parts of my org-mode tree (and Emacs' undo system, combined with org-mode's partial view of the tree, makes understanding what happened, or fixing it, extremely hard).
How can I find and disable all key bindings related to archiving, completely?

A: To find commands, C-h a (apropos-command) is often helpful. It will ask you for a regex and will return all commands that match the regex. So if you type the following: C-h a ^org-.*archive
you will get a list of commands starting with "org-" and containing the word "archive".
That said, checking the source as @lawlist suggests is of course better as commands are not always named the way one expects, though you here need to sift through not just the commands (ie those that can be bound to key combinations) but also all of the helper functions.
Other ways to quickly get to source files is, if you know of a specific command, to type C-h k and the key combination. This will bring up the help for that function, and from there you will normally find a button that brings you to the source file contains that command (provided emacs knows where it is).
There is a sister command to 'command-apropos' which is just named 'apropos'. This will search among all commands, functions and variables.

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The first dinosaurs lived near the end of theTriassic. Eoraptor, a bipedal carnivore recently discovered in South America, is the earliest known dinosaur.
Triassic dinosaurs have not yet been found in Utah. Late Triassic rocks known as the Chinle Formation are exposed throughout southern and eastern Utah. This rock unit has yielded abundant remains of the carnivorous (meat eating) dinosaurCoelophysis in Arizona and New Mexico. However fossil skeletons of other animals are known from Utah and it is only a matter of time before Utah's first Triassic dinosaur is discovered.


text:
Meaningful Melodies
Lyricist AM Turaz talks to Bhakti Mehta about how he weaves poetry into his lyrics to make beautiful songs like the ones in the upcoming Padmavati
Everybody is tripping on the soulful, folksy music of one of the most anticipated movies of the year, Padmavati. AM Turaz, the man who made us fall in love with the lyrics of this movie's touching songs, speaks about the overwhelming response he's received so far. "I want to thank Sanjay Leela Bhansali for giving me this platform through which my voice reaches the audience. The fact that the audience likes my work so much, makes me happy."
Going back to when the music of the film was still only being discussed, he says, "I was told that this is a period film and that I have to incorporate the culture in which it is set, into the music. A lot of hard work went into that. The songs had to flow with the narrative and, at the same time, be commercial. Although the audience has not yet watched the film, they are falling in love with the songs."
Turaz also reveals the research that went into bringing out the folk flavour in the lyrics. "As a poet, I have travelled not only all over the world but across India too, to beautiful, remote places. In Rajasthan, I met a few people from whom I learnt about the importance of the song Ghoomar. Even the Internet provides loads of information regarding these topics now. All that came in handy. The film is set against a Rajasthani backdrop, so my work was leaning organically."
On his hat-trick of collaborations with Bhansali, the lyricist remarks, "This is the third time I have worked with Mr Bhansali after Guzaarish and Bajirao Mastani. He made his debut as a music director in Guzaarish, which was my first film with him. So our journey kind of began together. He knows what I can do. He has an extraordinary talent to make these amazing films. As a music composer, he is fantastic."
Turaz says it helps that Bhansali understands his poetic bent of mind. "I write the lyrics first, then he makes the music for it. These days, it's the other way around, where the music is composed before the lyrics are written. Every aspect of his film has a theraav, which is very good for poetry to flourish."
Talking about the yet-to-be-released songs from Padmavati, the musician says, "All the other songs composed by Bhansaliji are perfectly set in the movie. A lot of hard work has gone into it and they will exceed the expectations of the audience as they release, one by one."
Composer-singer Rahul Jain and actor Sooraj Pancholi are Shining Bright with Dim dim light
When lyricist Raj Shekhar's dreams came true...
Saand Ki Aankh, the story based on the lives of sharpshooters Chandro and Prakashi Tomar, will be releasing this Diwali.
Sukh-E Muzical Doctorz talks about his recent single Wah wai wahh


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March 1, 2018 Cinema Bravo Event
Football for a Better Life launches partnerships, unveils Simone Rota docu
When the documentary "Journeyman Finds Home – The Simone Rota Story" was unveiled at the Uptown Ultra Cinema in Taguig, the event also marked the partnership of Football for a Better Life with other sports development programs. The film is presented by Davao Aguilas FC.
Football for a Better Life (FFABL), which aims to empower the youth and uplift their lives through the sport of football, is the main proponent of the documentary. Co-directed by Albert Almendralejo and Maricel Cariaga, the docu chronicles the personal struggles of Azkals' player Simone Rota— from how he was adopted by an Italian couple, to how grew up and played football in Italy, and then returned to the Philippines to join the national team and search for his biological mother.
Since the "Journeyman" work-in-progress was shown last September 2017 at the Cine Europa Film Festival in Shangri-La Mall, the filmmakers have added new footage and interviews. Says Albert Almendralejo, "We have added the grassroots programs that led to the establishment of the Youth Football League and included the Azkals game where Simone was called back to the national team. There is also new information about the lady whom Simone believed was his long-lost mother."
The premiere event also presented the two sports programs that FFABL is supporting: Women Empowerment through Sports (WEtS), an international youth project whose local organizer is the NGO Bridging the Gaps, and Mindanao1 Futbol, a talent identification mission in Mindanao led by national player-turned-coach Percy Guarin.
"Sport empowers women and develops values in children. This is the advocacy of Football for a Better Life and serves as our humble contribution to national development," states FFABL founder and president Mr. Almendralejo.
"Journeyman" is set to compete in the European Philippine International Film Festival, which will be held from March 7 to 9 in Florence, Italy. "Journeyman" is also slated to screen in the Sinag Maynila Film Festival, and in the 17 regional football association areas where the Mindanao1 Futbol talent identification search are being conducted. "We are happy to offer all proceeds of the Simone Rota special film screenings to endeavors that promote sports to women, kids and orphans, particularly to Women Empowerment through Sports, Mindanao1 Futbol and Buklod Kalinga sa Kapwa Foundation," says Mr. Almendralejo.
In a statement, Bridging the Gaps (BTS) said that the support is a boost to their goal of "developing, testing, and spreading new educational methodologies for young women empowerment through sports…" BTG has chosen Simone to be an ambassador of their cause.
For Coach Percy Guarin, the tie-up with FFABL complements his program's vision. "That is to touch lives through football and give kids plenty of opportunities to play and express themselves and discover new skills." In particular, Coach Percy said that the "Journeyman" docu is going to be an inspiration. "Seeing the movie of Simone will give children hope that someday their dream will be a reality." The film is supported by the Philippine Italian Association, Elan Vita Diagnostic Solutions and Puma.
Tagged Football for a Better Life, Journeyman Finds Home – The Simone Rota Story, Movie, Sinag Maynila, Sinag Maynila 2018
Life-like animation tricks the eye in 'Peter Rabbit'
'Pacific Rim: Uprising' launches banners of hero Jaegers


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The Race to Saving the Ocean Calls for "Super Action"
byIan Udulutch
Israel's UN Delegation Holds Its First International "Cyber Summit"
Public and private sector representatives will discuss ways to increase cooperation
UN Peace Advances in Colombia, but What About the Truth for Mario Paciolla?
The Security Council approves Resolution 2673 and Carlos Ruiz Massieu, head of the UN Verification Mission, responds to our questions
Quality of Life and Work Balance in the Post-pandemic World
A report conducted by the International Labour Organization, "Working Time and Work-Life Balance Around the World", is the first of its kind to measure work-life balance as it relates to economic development. The findings expose the effects of working hours...
Today's UN, Abysmally Humiliated, Needs Another Pérez de Cuéllar
byRenzo Cianfanelli
Guterres and Putin would do well to take a leaf out of his book to end the war in Ukraine
Another Climate Summit? "No-Nonsense, No exceptions, No Compromises"
Action must remain at forefront of global leaders' agendas
U.N. Report Calls for 20 Million New "Green" Jobs by 2030
"The cost of inaction is far greater than the cost of action"
Global Debt Crisis Traps Developing Countries in a Vicious Cycle
UNCTAD Secretary-General Rebeca Grynspan spoke at the 13th International Debt Management Conference in Geneva on Monday delivering a message on the state of the debt crisis in developing countries. "Geopolitics, not economics, is now in the driving seat of globalization,"...
UN Secretary-General: "We Are Waging War on Nature"
UN Secretary-General, Antonio Guterres, delivered a powerful speech at the opening ceremony of the UN Biodiversity Conference in Montreal on Wednesday demanding a fight for the survival of the global ecosystem, "This conference is about the urgent task of making...
The Swimmers: The Netflix Biodrama of Two Sisters' Harrowing Journey to Safety
Unlike the refugee crisis depicted in the mainstream media, the first scene of The Swimmers, written and directed by Sally El Hosaini, depicts the familiarity of adolescence as the Mardini sisters, Yusra and Sara, play in a neighborhood swimming pool....
U.N. on Racial Relations in Sweden: Safety Should not Rely on Over Policing
Sweden and the Scandinavian countries are generally viewed as paradigms of order and security. This may not be true. While anecdotal reports of social relations in Sweden are mostly positive, a recent report by the UN suggests that there is...
Women Leaders' Open Letter to UN: Ban Iran from Commission on Gender Equality
In an open letter published in numerous media sources this Sunday, a group of influential women called for the removal of the Islamic Republic of Iran (IRI) from the United Nations' Commission on the Status of Women (CSW). Since its...
Space for Our Planet: at the United Nations the Exhibition for a Sustainable Earth
A new multimedia exhibition, "Space for our Planet", opened Wednesday, 26 October 2022, at the Visitors Centre of United Nations in New York. The exhibition aims to introduce people to the solutions that Space activities can provide for ecological transition...


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Home Breaking News Lankan boat people killed
Lankan boat people killed
10 May 2010 02:26 am - 19 - {{hitsCtrl.values.hits}}
Australian authorities today said that five Sri Lankan asylum seekers are presumed dead after their boat went missing last week. The 'Australian' website said that a search and rescue operation for the missing Sri Lankans has been called off.
The men were traveling on an asylum boat carrying more than 60 people, including about 15 children, which was foundering 160 nautical miles west of the Cocos Islands.
On Wednesday, Customs and Border Protection Command alerted the Australian Maritime Safety Authority that the boat, which Customs had been tracking, was missing.
An RAAF P3 Orion, a Border Protection Command Dash-8 and a rescue Dornier aircraft scoured a 33,000-square-nautical-mile search zone, about 270km northwest of the Cocos Islands.
The following evening, the boat was found drifting, its engine disabled. Four merchant vessels in the vicinity were sent to its aid and eight of the boat's passengers were taken aboard a Russian bulk carrier, the MV Postojna. The rest stayed on the boat as a ship towed it to the Cocos Islands. Asylum-seekers told the crew that three days earlier, five male passengers had donned life jackets and jumped overboard in an apparent attempt to swim for help.
A search-and-rescue operation began the next day but failed to find the men. However, a spokeswoman for Home Affairs Minister Brendan O'Connor said items that "may have been associated with the persons missing" - life jackets and tyre tubes - had been found.
The spokeswoman said yesterday the search had been called off.
"The search has now been discontinued on the basis of medical advice that chances of survival were no longer a reasonable possibility."
Mr O'Connor said the "tragic" incident underscored the folly of trying to travel so far to Australia in poorly maintained boats.
The asylum-seekers' boat was yesterday towed to the Cocos Islands, from where its passengers will be flown to Christmas Island.
Authorities were last night preparing to interview the 59 remaining passengers in an attempt to identity the missing men and explore what happened.
The location of the incident suggests they sailed directly from Sri Lanka. Thursday's rescue was not the first time the boat had received assistance. The same Russian ship gave those on board food, fuel and water after Customs made contact with the vessel on April 30.
A spokeswoman for Mr O'Connor said at that time the boat had been judged seaworthy, the Australian reported.
Monday, 10 May 2010 04:57 AM
Imagine the sense of relief when they set off on that boat, and how their dreams and hopes must come to life again, How can we hope to attract people to our country when we can't even hold onto the ones who are already here.
Tuesday, 11 May 2010 01:51 AM
Please do not come to Australia to ruin our reputatuion
There are the people who supported Tigers. These are the people who worked for (Make shift)Tiger government. But did not last long. I remember how they tried to tax me for my apples, when I was travelling to Jaffna.
Good if they leave SL, they can get rid of terrorists, not good for Aust, they may start Aust.Elam for tiger terrorist.
You have dug your own grave. SUFFER...................
There is no different in policy to discriminate Jaffna Tamils, between TN and SL governments.
Any decent human would like to get out of SL, because it's not a place to live a normal human life.
Perhaps they travel all the way to Australia is because they welcome asylum seekers with open hands.
Hello Sam, stop judging innocent tamil who are trying escape. if they are LTTE supporters you are a sinhalese terrorists supporter
no where sir, just a common sense !
Its not about betterment. you can make a better place for you even in India. Why go all the way to Australia. Why not Malaysia or even Singapore? This nation is Indeed a Miracle of Asia. The tourist arrivals have increased by 50% over the last year. Go to the villages and see the development.... Dont just stay in Colombo and complain. Open your eyes and see. This is why the villages endorsed this government. Because they have seen.
They are LTTE supporters looking for greener pastures. I have no sympathy for them!
Local Boy: where did you read in the news item that these people were Tamils?
What risks they take to escape from the so called "Miracle of Asia"
It's simple local boy..... If you risk your life for betterment, ..aim for the best country in the world. ...Not for Parripu
What risks they take to creep into first world countries only, via the back door. Dont blame Sri Lanka for the follies of these economic refugees who are in possession of large amounts of money which they can easily afford to pay the people smugglers.
This is very unfortunate incident.i myself am an Australian Citizen.My citizenship has been granted against my off shore research contributions.In terms of standard of living Australia, it is neither a heaven nor exceptional from rest of the world..Satisfaction in life is purely based on your mental set up.- in other words based on your expectations in life.Situation is like caught in between the deep sea and the devil.But here there is no real threat for Tamils in Lanka after the post war except from their own Tamil politicians.
If anyone is trying to escape from Srilanka facing this dangerous way, our Government should know there are some problems in our mother land to solve immediately. Otherwise we can't make so called "Miracle of Asia".
Srilanka is a nature's paradise. There is no doubt on it. It has everything other than peace.
The question arise's why still people (mainly Tamils) are trying to escape from Srilanka?
One year back LTTE has been defeated by Srilankan government but until today there is not a single step taken by the government to resolve the ethnic conflict.
For Tamils it looks like Srilanaka has gone back to 1950's, that is the time when the ethnic conflict started.
Yes if there is no solution found, definitely there will be another ethnic war starting
there are NO genuine Sri Lankan refugees. they are all bogus 'economic refugees'
Very sad. Please look in to this in human point of view rather than going to the extent of politics.
'Calistus Jayatilleke' why do not they go to India? just a few Km away from here? TN speaking same Lan? Why take such a risk? Mr. above slogan is just a promise made by president. you've got to wait and see for next six years.


A pipe burst Monday afternoon at the University of Calgary, as students were travelling between classes causing water to spray down from the ceiling.
The U of C says a sprinkler line break occurred in the link between Science A and Science B.
Calgary fire responded to block off the area and ensure staff & Students safety. No one was injured.
The leak comes during Calgary's chilliest day in over a year, with the coldest wind chill values ranging between -40 and -45 C.
Classes are scheduled to resume Tuesday morning.


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The hotel is just a five-minute walk from Green Park tube station, but feels a world removed from Piccadilly's frantic foot traffic.
The building sits adjacent to glitzy fashion boutiques and jewellers; right across the street is Royal Arcade, a Grade II-listed Victorian shopping arcade lined with expensive shops, including a chocolatier that currently holds the Royal Warrant.
Buckingham Palace and St James's Palace are less than a 15-minute stroll away, as are the exclusive members' clubs of Pall Mall.
Simply put, this is a fine base to experience one of London's poshest – and most storied – postcodes.
Each room and suite is individually decorated and many feature original and contemporary works of art, creating an elegant and fashionable air.
The Donovan Bar and Beck at Brown's celebrate Italian art and cuisine, while the award-winning afternoon tea is a quintessentially English Experience.
In the heart of fashionable Mayfair, Brown's Hotel is just a short walk from luxury shopping streets, theaters, art galleries and key central London landmarks.
Jet boat on the Thames
Roar up the Thames from Chelsea Pier to Canary Wharf on a chartered Royal Marines assault craft and you'll get a unique perspective of London landmarks from the water.
The Old Truman Brewery
This beautiful old brewery founded in the 17th century now houses more than 250 businesses, ranging from cultural venues to art galleries, restaurants and retail shops. 91 Brick Ln.
With its spectacular panorama of the Thames and the London skyline, Skylon is a convivial and scenic South Bank spot for a cocktail or dinner. Third floor, Royal Festival Hall.
Famous for its market and diverse cultures, this East End neighborhood has undergone an amazing renaissance and now presents an eclectic range of restaurants, shops, galleries and historic streets to explore.
Tramshed
The latest addition to the Mark Hix restaurant empire, this trendsetting restaurant in a converted tramshed in Shoreditch presents a simple menu of sumptuous steak or chicken. 32 Rivington St.
This seafood restaurant in Mayfair serves the finest oysters, fish and seafood, all responsibly caught from sustainable sources. The menu also offers seasonal game, meat and vegetarian dishes. 20 Mount St.
Hakkasan Mayfair
Hakkasan is a lively fine-dining restaurant with a Modern Chinese menu that includes dim sum, stir fries, soups and updated Chinese specialties like Peking Duck. 17 Bruton St.
At Bertram's Hotel
Agatha Christie regularly stayed at Brown's Hotel and based this novel on the property.
Shaped like an irregular glass pyramid, this 1,020-foot-high (310-meter) office tower was designed by Renzo Piano and is the tallest building in London. There's an observation platform on the 72nd floor. 96 Tooley Street.
Tea from Fortnum and Mason
Have a look around this historic store on Piccadilly—it holds two Royal Warrants and serves as the Queen's grocer—and buy a tin of your favorite tea. 181 Piccadilly.
In the heart of London's elegant Mayfair, Brown's Hotel is an iconic luxury hotel where history and 21st century sophistication come together. The retreat of choice for royalty, presidents and literary greats over the centuries, Brown's Hotel is an enduringly distinguished destination in London. Unmistakably British, our inviting rooms and luxurious suites offer exceptional comfort and style, marrying heritage features with contemporary touches. Our warm, personal service will make you feel right at home. During your stay, enjoy a quintessentially British Afternoon Tea in The English Tea Room, savour fine cuisine at The Restaurant at Brown's, sip cocktails after dark at the chic Donovan Bar and surrender to bliss at The Spa at Brown's.
Located in London's most exclusive borough, Brown's Hotel is a microcosm of chic, modern and arty Mayfair making it the ideal base for luxury travellers. Moments from the fashion houses of Bond Street, in one of the world's leading art districts and within walking distance of five royal parks, Brown's Hotel is at the centre of London's finest experiences.
Compared to the distinctive and ornate restaurant and public area, the rooms feel a bit sedate and uninspiring. Greens and yellows are the dominant hues, contrasting nicely with with calabash-shaped glass lamps. Large mirror wall panels add light and dimension to the room, and there is lots of bulky, brown furniture. The main category is the Executive rooms, which are spacious by London standards, with lots of storage space, a desk and sofas. The historical-themed suites have impressive artefacts on display – such as letters written by Kipling or the telephone used by Alexander Graham Bell.
Our spacious Classic Rooms offer comfort and style, marrying timeless English elegance with flashes of modernity. British artworks lend a touch of personality while a sumptuous queen-size bed invites restful sleep. Furnished with a desk, they're perfect for business travellers. The beautifully appointed marble bathrooms feature a bath and shower with our pampering Forte Organics toiletries.
Our generous Executive Rooms combine an elegant bedroom with a stylish sitting area. British sophistication and contemporary design harmonise with vibrant, colourful textiles, while assorted books nod to Brown's Hotel's literary heritage. The fine marble bathrooms feature a bath and shower along with our pampering Forte Organics toiletries.
Each of our expansive Deluxe Rooms has its own distinct identity. All offer exceptional comfort and space with inviting open-plan sitting rooms, walk-in wardrobes and generous working areas. Perfect for longer stays and families, our Deluxe Rooms can be interconnected with Executive Rooms and other Deluxe Rooms. The beautiful bathrooms feature a bath and shower along with our pampering Forte Organics toiletries.
Our airy and bright Junior Suites are exquisitely decorated in soothing slate and grey tones with lively pops of burgundy and ochre. Each features an inviting king-sized bed, open-plan living area and generous walk-in wardrobe. A calming retreat in the heart of the city, our Junior Suites overlook stylish Mayfair, historic Albemarle Street or our inner courtyard. The tranquil bathrooms feature a bath and walk-in shower alongside pampering Made for Life 100% organic toiletries.
Studio Suite
Our spacious and contemporary Studio Suites are inspired by our British heritage and accented with shades of moss green and azure blue. One-of-a-kind ornaments from local designers adorn the suites and a library of English classics complements the hotel's literary past. A generous, open-plan sitting room is the perfect place to unwind, while a comfortable king-sized bed or twin single beds welcome a sound night's sleep. The Studio Suites bathrooms feature a bath with built-in television, a walk-in shower and indulgent Made for Life 100% organic toiletries.
Brown's Suite
Our nature-inspired Brown's Suites are exceptionally spacious, featuring a stylish bedroom with king-sized bed and walk-in wardrobe, a separate sitting room and two bathrooms. Moss and sage green tones, beautiful oak wood flooring and treescape Lewis & Wood wallpaper invoke a sense of natural calm as you make yourself at home. Adjoining the bedroom, the bush-hammered limestone bathroom has a generous bath and walk-in shower while the Bisazza mosaic bathroom features a marble vanity unit.
Classic Suite
Our lavish Classic Suites are unmistakably British with stylish ornaments and art from local artisans and quintessentially English books tastefully accenting the space. Comprising a large separate sitting room and elegant bedroom with king-sized bed, our Classic Suites overlook the glamorous boutiques of Albemarle Street. Perfect for families, the suites can accommodate an extra bed and be interconnected with a neighbouring suite. The immaculate bathrooms feature a bath with a built-in television, a walk-in shower and indulgent Made for Life 100% organic toiletries.
Our grand Deluxe Suites are exquisitely appointed and spacious, featuring a large sitting room and dining area and a welcoming bedroom with a king-sized bed. Enlivened with burgundy and scarlet tones and showcasing distinctly British artefacts, the modern suites are stylish and inviting. Perfect for families, our Deluxe Suites can accommodate an extra bed and be interconnected with neighbouring rooms. The large bathrooms feature a bath with a built-in television, a double shower, double washbasins and indulgent Made for Life 100% organic toiletries.
Dover Suite
The stately Dover Suite conveys a sense of understated elegance. Floor-to-ceiling windows overlooking its namesake, Dover Street, bathe the suite in natural light. Lustrous gold and green fabrics in tactile textures enrich the suite's muted shades. Ornate cornicing, an imposing marble fireplace and antique furnishings harmonise with contemporary touches and artworks. This sophisticated suite features a large sitting room with dining area and a beautifully appointed bedroom with a king-sized bed. The spacious bathroom features a bath with a built-in television, a double shower, double washbasins and indulgent Made for Life 100% organic toiletries.
Hellenic Suite
The impressive Hellenic Suite is perfect for families. Beautifully mixing classic British heritage with modernity, the spectacular suite showcases stunning antiques and contemporary artworks, evoking a quiet opulence. Overlooking stylish Dover Street, floor-to-ceiling windows flood the suite's caramel tones with natural light. This distinguished space features an imposing sitting room with its own dining area and an exquisitely appointed, spacious bedroom with king-sized bed. The Hellenic Suite can combine with neighbouring rooms to create a three-bedroom suite. The expansive bathroom features a bath with a built-in television, a double shower, double washbasins and pampering Made for Life 100% organic toiletries.
Kipling Suite
Named after esteemed author Rudyard Kipling, who penned TheJungle Book at Brown's Hotel, the Kipling Suite is our most distinguished residence. From the cheeky monkey statue outside the door to a framed handwritten letter from the author himself, there are playful nods to Kipling throughout. A grand entrance hall leads to the commanding sitting room, which beautifully marries period features and antique furnishings with contemporary style. The stunningly appointed bedroom with king-sized bed and walk-in wardrobe is accented by gold and green hand-painted Lewis & Wood wallpaper and one-of-a-kind artwork. Floor-to-ceiling windows overlook historic Albemarle Street's designer boutiques. The Kipling Suite's luxurious Italian Arabescato marble bathroom features a freestanding bath, a double shower, double washbasins and indulgent Made for Life 100% organic toiletries.
If you are to only have one meal at Brown's, make it dinner at Beck. Every dish is lavishly presented, but the stars of the menu are the primis: the fagottelli alla carbonara is an unctuous treat, revealing a soup of egg yolk, black pepper Parmesan and pecorino cheese as soon as you bite into the delicately folded dumpling. The black truffle risotto – dotted with seasonal veggies and shaved black truffle – is one of the best I've ever tasted. Other highlights include a French pigeon dressed with salsify roots, and a firm but crispy dover sole grilled with lemon.
The Restaurant at Brown's
Welcome to The Restaurant at Brown's, a stylish dining destination set in London's first hotel. Here, in the heart of Mayfair, discover a new, creative menu showcasing the finest elements of contemporary British cuisine with a hint of European flavour. Served throughout the day, dishes are freshly crafted and presented with flair and passion, complemented by the service Brown's is so famous for. From September, Brown's is delighted to welcome Adam Byatt, chef-owner of Michelin-starred London restaurant Trinity, to the hotel as its new Chef Director of Food & Beverage.
The Donovan Bar
Intimate sophistication. Playful decadence. Scintillating cocktails. The Donovan Bar has long been the destination of choice for Mayfair's most discerning sippers. Inspired by its namesake, celebrated photographer Terrance Donovan, this stylish drinking den is adorned with his iconic 1960s prints and sleek, photography-themed accents. The Donovan Bar's impeccable cocktail menu comes courtesy of the legendary maestro of cocktails, Salvatore Calabrese—who has created a sublime list marrying his personal classics with original concoctions.
Relax with an aperitif, savour mouth-watering bar snacks or enjoy an after-dark libation tucked away in the Donovan Bar's 'Naughty Corner'.
The English Tea Room
With original wood panelling, striking contemporary artworks and a genteel ambience, our London tea room is a place where quintessentially English sensibilities and modern sophistication harmonise. Follow in the footsteps of royalty and indulge in neatly crimped sandwiches, the daintiest of pastries and pillowy scones stuffed with fresh cream and jam. Peruse our menu of 17 fine teas and unwind in the English Tea Room's grand surroundings.
The staff clearly take pride in working at a heritage hotel and know the building inside and out; they are more than happy to give tours of some of its fabled suites (even to non-guests) if available. Reception is extremely professional and always assure that every need is taken care of, and will promptly send handwritten notes if problems arise. The staff at Beck are equally zealous, and the executive chef will personally greet each table and ask for their thoughts on the cooking at the end of dinner. Service at Donovan Bar, however, was less warm. There's a small spa and 24-hour gym in the basement.
Soothe your senses at our tranquil spa. A subterranean sanctuary in the heart of London, our highly skilled therapists will help you relax with a pampering beauty treatment or restorative massage, using the finest organic products. We invite you to balance mind, body and spirit with one of our signature Forte Organics Rituals, enjoy an indulgent manicure or drift into bliss with a hot stone treatment. One of the best spas in London, The Spa at Brown's offers the bespoke Irene Forte Skincare range, made from natural, mineral-rich ingredients grown at our Verdura Resort in Sicily.
Our gym is open 24 hours a day and provides a range of the latest Technogym cardiovascular, weight and resistance equipment.
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Thoughts!
Lost in Criterion
Cinema Credo
Lost in Criterion is a podcast by two old friends on opposite sides of the world who decided to challenge themselves to do an impossible task: watch every movie in the Criterion Collection and discuss them with each other.
The Complete Monterey Pop Festival
February 19, 2016 Adam Glass
At the height of the Summer of Love powerhouses in pop music came together to hold the first Monterey Pop Music Festival, possibly the first pop music festival ever. D.A. Pennebaker was on hand to record the proceedings to be released as a film, though his footage was eventually released as three. We're talking all of them on this week's Lost in Criterion, including supplemental materials, as we explore the Complete Monterey Pop Festival box set containing Monterey Pop (1967), Jimi Plays Monterey (1986), and Shake! Otis at Monterey (1986).
Tags d.a. pennebaker, monterey pop, the complete monterey pop festival, monterey pop festival, jimi plays monterey, shake! otis at monterey, 1967, 1986, united states, documentary
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Do you need a reputable plumbing company to provide water filtration services in Bonney Lake, WA? If yes, then contact Beacon Plumbing because they offer exceptional water filtration services to residents of Bonney Lake at very low prices.
All of these issues can be handled very easily if you hire our experts of water filtration for your Bonney Lake property. If you care about your family, and wish to make the water you receive in your house clean, as well as healthy, then it is very important you hire our services as soon as possible.
Our trusted water system installation and repair services can purify the water you use in your Bonney Lake property right from the mains. Once we finish our job of water system installation and repair in your Bonney Lake property, the hot and cold water will be filtered thoroughly so that you have absolutely clean water for your use.
Hence, our water system installation and repair can make sure that harmful pollutants do not harm your skin or your health when you use it.
The experts we employ can also install well pumps in Bonney Lake properties. Our well pump installation service can be useful to Bonney Lake residents if they depend on well water.
Our professionals have comprehensive knowledge of this field, making their service unmatched in the area.
Dial 800-373-2546 to employ our water system installation and repair services. Beacon Plumbing offers impeccable water filtration and well pump installation services to Bonney Lake residents.