text:
US Army wants to use a soldier's FOOTSTEPS to power electronics and let commanders track them while they are on the battlefield
US Army is developing insoles with sensors to power electronic devices
The heel pushes down on the insole and hits a miniature rotational mechanism
This then turns a small generator and creates an electric charge
The electricity would also allow commanders to track a soldier's location
By Stacy Liberatore For Dailymail.com
Published: 14:10 EST, 24 December 2019 | Updated: 17:12 EST, 24 December 2019
Soldiers are increasingly reliant on electronic devices in battle and scientists believe they have found a way to keep them charged without the need of an outlet.
The US Army is working with Robotic Research LLC to design sensor fitted insoles that would generate electricity each time the wearer takes a step.
The technology would not only power technology, but also allows commanders to track their soldiers in GPS-denied environments.
Robotic Research LLC, a leading provider of autonomy and robotic technologies, was recently awarded a $16.5 million contract from the US Army to develop the sensors using its technology called WarLoc.
The insole technology was found in a patent out of the Army's C5ISR Center, which will create electricity through the wearer's footsteps.
Soldiers are increasingly reliant on electronic devices in battle and scientists believe they have found a way to keep them charged without the need of an outlet. The US Army is working with Robotic Research LLC to design sensor fitted insoles that would generate electricity each time the wearer takes a step
When a soldier's heel pushes down on the insole, the force hits a miniature rotational level mechanism and turns a small generator, which creates an electric charge, the Army Times reported.
Nathan Sharpes, a C5ISR Center mechanical engineer who developed the patent, told techlinkcenter.org: 'We embedded an energy-harvesting mechanism into a combat boot heel insole so that each time a soldier's heel strikes it activates a generator, which spins to produce energy.'
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The US military is constantly looking for new ways to produce electricity for troops on the battlefield.
In 2017, scientists were testing ways to lighten the load created by batteries, which are often as heavy as the equipment they keep charged.
When a soldier's heel pushes down on the insole, the force hits a miniature rotational level mechanism and turns a small generator, which creates an electric charge
The researchers found one of their experimental materials was generating high amounts of electricity when in contact with water.
The revelation could provide new ways for soldiers to power equipment on the battlefield as well as commercial products to power our electronic gadgets.
Laboratory at the Aberdeen Proving Ground in Aberdeen, Maryland, stumbled upon the surprising property after an aluminium based powder began to bubble in water.
They soon realized the reaction was the product of hydrolysis, a process which breaks down water into it its constituent parts of oxygen and hydrogen.
The hydrogen that is given off can be used in a fuel cell.
And the team put this principal into practice by powering a small radio-controlled tank with the powder and water reaction.
Moments after mixing the powder with a small amount of water, a bubbling reaction produced a great deal of hydrogen, which was then used to power the model around the laboratory.
And in 2016, the US Marines announced they were testing new pants that would provide power on the go.
Called PowerWalk, this light-weight, leg-mounted design harvests energy from the natural action of walking.
The US military is constantly looking for new ways to produce electricity for troops on the battlefield. In 2016, the US Marines announced they were testing new pants that would provide power on the go
Users can generate 10 to 12 watts while wearing the device and after an hour-long walk, they can create enough electricity to charge four smartphones.
PowerWalk is the brainchild of Canada-based Bionic Power, which developed the exoskeleton to help reduce the number of batteries soldiers need to carry on missions to provide more space for essential field gear.
'A soldier typically carries 16-20lbs in batteries on a 72-hour mission,' says Noel Soto, U.S. Army Systems Engineer at the Natick Soldier Research, Development and Engineering Center.
'If a soldier can generate power with wearable energy-harvesting devices, it means we can not only reduce the weight on his or her back, we also minimize the unit's reliance on field resupply, making it possible for us to extend the duration and effectiveness of a mission.'
A gearbox transforms the knee's rotational speed to a higher speed for efficient power generation and a generator converts the mechanical power into electricity.
Then a 'state-of-the-art power-conversion' circuit converts the electricity for battery charging which gives proves the charge for Li-ion or NiMh batteries.
HOW IS THE US MILITARY HOPING TO 'HACK' SOLDIERS BRAINS?
Darpa's four-year Targeted Neuroplasticity Training (TNT) program aims to use the body's peripheral nervous system to accelerate the learning process.
This would be done by activating a process known as 'synaptic plasticity' – a key process in the brain involved in learning – with electrical stimulation.
Some teams will be working with intelligence analysts and foreign language specialists to shape the platform around currently training practices.
Researchers will look into using the technique across a wide range of applications, including decision-making and spatial navigation, speech perception and threat recognition.
'Imagine you're struggling to learn something new, like multiplication tables or how to hit a golf ball,' said Dr Robert Rennaker, of the University of Texas at Dallas' Texas Biomedical Device Center.
'When you get it right, when that light bulb comes on, this system is being activated.
'By stimulating the vagus nerve during the learning process, we're artificially releasing these chemicals to enhance those connections active during learning.'
How the Army wants to use your boots to generate juice (and keep tabs on you)
US Army wants to use a soldier's FOOTSTEPS to power electronics while they are in the battlefield
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У̀рас (; ) е малко градче и община в Южна Италия, провинция Ористано, автономен регион и остров Сардиния. Разположено е на 23 m надморска височина. Населението на общината е 2980 души (към 2010 г.).

Източници

Външни препратки

 Уебсайт на общината

Ористано (провинция)
Градове в Сардиния

redpajama_set_name: RedPajamaWikipedia


One of the things nature teaches us is the meaning of giving. The commanding mountain springs of Zagorochoria generously provide Natural Mineral Water. Let us find it in ourselves to offer a little hope to those in need.
...and continue giving to those in need!
"Vikos" Natural Mineral Water is pumped straight from the source in the famous district of Zagorochoria, a residentially and environmentally protected area.
From its pumping until its distribution to the end consumer, "Vikos" Natural Mineral Water does not undergo any processing.
Vikos Natural Mineral Water is brought via a stainless steel network of pipes to the latest bottling machinery (close to the source) without undergoing any processing.
Its underground route through Limestone rocks enriches it in precious minerals giving it a perfectly balanced composition..
Epirotic Bottling Industry S.A. (Vikos S.A.) was founded in 1990 and is one of the most renowned and established companies in the bottled water market.
Vikos S.A. operates 4 modern factories that have a vertically integrated manufacturing process, on its own premises, a total surface of 65.800m2, in an area of 223 acres.
VIKOS SA, in response to modern nutritional trends, launches three new products with a sweetener from the stevia plant: Vikos Orangeade, Vikos Lemonade and Vikos Cola.
VIKOS S.A. supports "G. Hatzikosta" General Hospital of Ioannina.
Manufacturing new products according to the increasing demands of the modern market.
The company has been certified by Lloyd's Register for its Quality Assurance Management Systems.
At Vikos, the notion of volunteering has a special meaning for us, not in theory but in practice.


Pilgrim United Church of Christ – You are welcome here.
Welcome to Pilgrim Church, an open and affirming community within the United Church of Christ with a progressive theology, a commitment to spiritual growth and passion for social justice. We gather to seek after the mystery of our faith, seeking to create a safe space where we can rejoice, suffer, heal, and hope together. Pilgrim is an inclusive community where all persons are welcome. Progressive Theology leads us to explore new ideas about God, new understandings about Jesus and a fresh take on our ancient texts that speak to our present moment. We preach and teach and sing and serve in a variety of ways that allow us to demonstrate our values.
We are a multi-racial, multi-generational church that seeks to offer everyone God's extravagant welcome. We would love it if you would join us for a time of worship, music, and fellowship on Sunday morning at 10:00 am in Carlsbad.


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The technology of food and drink in focus at fdt Africa 2019 food & drink technology Africa (fdt Africa) will return to Johannesburg next year, bringing to sub-Saharan Africa the full lab to table value chain in the food, beverage and the respective packaging industry.
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Supply chain professionals to meet at SAPICS Case studies and advisory sessions of special relevance to the pharmaceutical, cosmetics and related industries will be a featured on the programme of the 38th annual SAPICS Conference and Exhibition, taking place from 12 to 14 June, at Sun City.
Two ways COVID-19 affects financial advisers (and it's not just income) By: Hannes van den Berg, Chief Executive Officer of Momentum Consult As financial advisers you're at the coalface of the industry. Even though you project a strong, confident energy when you deal with clients you also have fears and anxiety to deal with. But the good news is, these concerns can be addressed and, if...
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Survey finds that Gen Z and Boomer consumers differ vastly Generation Z consumers are more concerned about the sustainability credentials of food and beverage products than Boomers, and find vegetarian and vegan products more appealing, new research shows. It's important to align product development and marketing with the worldview of your target demographic. Vegan claims are very appealing PR company Ingredient Communications surveyed 1 000...
RCL Foods turns to Schneider Electric to modernise Pongola mill operations When Durban-based RCL Foods embarked on a modernisation journey at one of its three sugar mills, it turned to Schneider Electric.
The South African Wood, Laminate & Flooring Association The South African Wood, Laminate & Flooring Association (SAWFLA) was formed to enhance awareness of wood and laminate flooring products, to protect the end user and the environment and also for education, industry players throughout the supply chain. SAWFLA collectively addresses topics facing the wood and laminate sector. The highlighted benefits include accreditation sessions, use...
Companies should be more proactive in fighting corruption Organisations are not immune to the devastating consequences of fraud and corruption. Nowadays, organisations are under threat from a host of risks including procurement fraud and cybercrime. Zaakir Mohamed, Director in the Dispute Resolution practice at Cliffe Dekker Hofmeyr (CDH), says that it is critical for organisations to fully understand the risks they face and...
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I'm sad to report that the deployment curse has decided to stick around. Only this time, instead of breaking material things, it has unleashed its power on our bodies!
If there is a physical ailment to be had, we've had it. Coughing, runny noses, ear aches, stomach woes, growing pains ... Our bodies have taken a beating.
I suppose it's the time of year for such things, so I'm trying not to take it personally. Unfortunately, the brunt of this physical attack hit during what will forever be referred to as "The Worst Vacation Ever." On our nine-hour drive to an indoor water park, two of my boys came down with terrible coughs and fevers. This was fun to endure while my GPS — which hates me, apparently — led me on a string of back roads to nowhere.
Once we finally arrived, we spent the first day in our hotel room watching cartoons. The second day, when the fevers had faded, was a blur of cough syrup, pain reliever and all the water-park fun their poor little bodies could muster. Until the coughing turned into severe sore throats. And then the stomach woes hit. And then, well, need I go on? The next couple of days were spent trying every home remedy we could find on Google.
The drive home was miserable, too. In the middle of a snowstorm, my windshield wiper broke. I can't make this stuff up.
At home, we were eager to move on and put the sickness behind us. But then my microwave broke. Now, that's just going too far. "The problem with your microwave was a fluke and rarely happens," the repairman told me. This was not shocking news. "Fluke" is my middle name.
If what doesn't kill you makes you stronger, I'm going to have some killer muscles when this thing is over. Life is bumpy and messy and just plain awful sometimes, but no matter the bad, I'll cherish the good. My husband makes this difficult time worthwhile. This country makes this difficult time worthwhile.
When Matt comes home, I'll hug him so very tightly with my newly developed Superwoman arms. Until then, I think I'll go buy an extended warranty for everything we own and make sure our insurance is up to date.


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The average price of homes for sale in Roswell is $518,794, with the highest listing price at $6,300,000 and a low of $1,050. The average listing price for Roswell is 54% more than the average of Georgia of $337,821.


At Adoption Makes Family we want you to be able to assist your child wherever possible and make for a strong, loving, and hopeful future for them, and we're willing to act as another resource to help during the process.ÂÂ We can help you create your own loving adoption plan and can essentially plan out the future your child would like to have and discuss ways of reaching these goals. We can provide you with the support and assistance whenever you may need it.
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Romans in Liverpool?
Roman Liverpool is a story shrouded in mystery. The Romans were definitely here but the exact degree to which no one can be certain of. This is because there are only very small fragments of evidence that have been found.
Coins, jewellery and pottery have been unearthed from all over Merseyside, especially across the Wirral. In particular the northern area of Meols where there was thought to be a shipping port.
In the 1850s parts of a Roman Road were thought to have been found in the areas of Aigburth and Otterspool, and several Roman coins were also found there also. A Roman Well (containing coins) was once found near in Halebank.
Some people believe the Romans called the Liverpool area Portus Segantiorum. This is because it is listed on a map based on the research of Roman Geographer Ptolemy.
However, Portus Setantiorum could be further north towards Fleetwood near Blackpool or even as far West as Meols on the Wirral? People over history have made differing claims.
Ptolemy's map also shows a river called Belisama, generally thought of as being the River Ribble and a river called Seteia, which could be the Roman name for the River Mersey, however, some think this could be the Dee.
Problems arise from the fact that Ptolemy based his 'locations' on other people's words (translated across different languages) and the map itself was not drawn until over well over 1000 since it he designed it.
It is possible that the Romans came to Liverpool on route from the larger Roman settlements at Deva (Chester) or Bremetennacum (Ribble Valley – Lancashire).
The question is, why didn't the Romans stop at Liverpool? Why did they just pass through it?
One theory that the River Mersey itself was not really exist in Roman times the way it does today and that it was created from an earthquake sometime after the Romans had left the area.
Several Victorian Canal engineers came to this conclusion when examining the Mersey and some of the known geology of the area.
There is archelogical evidence of an earthquake around this area around the 600s and that it may have moved a Stockport stream (which used to flow into the River Dee) into what is now the River Mersey.
Other factors that add to the confusion are the fact that the whole geography of the area was much different in ancient times with evidence that areas that are now sea and river were once land that people lived on.
Additional links about the Romans in Liverpool:
Pictorial Relics of Ancient Liverpool
Interview about Mersey Earthquake
Roman Wirral and Portus Setantiorum
Further Discussion on Roman Liverpool and the Mersey Earthquake
Add mini text here
Contact historyofliverpool@gmail.com


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\section{Introduction}

Spontaneous symmetry breaking is a key notion in particle physics and the symmetry can be either a kind of internal symmetry or a symmetry associated with spacetime transformations. Breaking of internal symmetries spontaneously causes topological defects which are called global. A general property of spontaneously broken global symmetries is the Goldstone degree of freedom which  in the monopole case results in a divergence of the total global monopole energy. In order to remove this self-energy problem one way is to introduce the self gravity of global monopole which is also essential for astrophysical applications \cite{Bronnikov}.
Monopoles which are formed by gauge-symmetry breaking during the phase
transitions in the early universe can be the source of inflation \cite{Preskill,Barriola}.
Monopoles are one of the example of stable topological defects \cite{Vilenkin:1981zs,Vilenkin:1982hm}.
On the other hand, global monopoles result from a global symmetry
braking of global $O\left(3\right)$ symmetry into $U\left(1\right)$
in phase transitions in the universe \cite{Vilenkin:1981zs,Vilenkin:1982hm,Vilenkin:1984ib,Vilenkin:1981kz}.
The effect of these monopoles on Schwarzschild spacetime are discussed
in \cite{Dadhich} by analyzing the particle orbit and Hawking radiation.
On the other side, the Lorentz symmetry breaking (LSB) is associated
with the idea that the Quantum Gravity (QG) signals may emerge at
low energy scales \cite{Cas}. The naturelness and the possibility
of Lorentz symmetry breaking is discussed in the context of string
theory in \cite{Kosteleck=0000FD-1,Kosteleck=0000FD-2,Kosteleck=0000FD-3,Kosteleck=0000FD-4,Kostelecky:2000ku,Kostelecky:2018yfa,Kostelecky:2002ca,Lehnert:2004be,Bertolami:2003qs,Diaz:2013saa,Kostelecky:2000mm,Lehnert:2018lce,RalfLehnert:2016grl,Cambiaso:2012vb,Lehnert:2011ed,Bluhm:2004ep}.
The Lorentz symmety breaking arises in other theories like noncomutative
field theories \cite{Carroll,Mocioiu,Ferrari} and loop quantum gravity
theory \cite{Gambini,Ellis} among other scenarios \cite{Berger,Blas,Lehnert,Gorbunov,Maluf:2021lwh,Oliveira:2021abg,Jha:2020qkm,Delhom:2021lxs,Delhom:2020gfv,Nascimento:2014vva,Assuncao:2017tnz,Assuncao:2019azw,Jha:2020pvk,Khodadi:2021owg,Ding:2020kfr,Chen:2020qyp,Ali:2020ddi,Ding:2021iwv,Carvalho:2021jlp,Ding:2019mal,Jesus:2020lsv,Oliveira:2018oha}.

Einstein's general relativity (GR) describes gravitation at the classical level. On the other hand standard model (SM) of particle
physics brings all other interactions together below the quantum level.
At the Planck scale, $m_{p}=10^{19}\;GeV$, these theories expected
to merge into one single unified theory which may provide a successful
description of nature. Altough, confirmation of this idea is compelling
because experiments at the Planck scale are unfeasible, the effect
emerging from the underlying QG theory might be observable at the
low-energy scales \cite{Cimdiker:2021cpz}. One way to set the framework of Planck-scale signals
is violating relativity and these violations are related to the breaking
of Lorentz symmetry. Theories violate the Lorentz symmetry at the
Planck scale and contain both GR and SM are effective field theories
known as the SM-Extension (SME) by which the observable signals of
Lorentz violation can be described \cite{Kostelecky-1,Kostelecky-0}.

Bumblebee models are effective field theories which
has a vector field with a non-zero vacuum expectation value (VEV)
that sponaneously breaks Lorentz symmetry \cite{Kosteleck=0000FD-3,Kostelecky:2000mm,Kostelecky-0}.
These particular type of effective field theories named by Kosteleck\'y
as Bumblebee models inspired from the real-life bumblebees. Real-life
bumblebees have a large bodies but tiny wings which give rise to think
bumblebees can not fly for a long time, however they can successfully
\cite{Dickinson}. Similarly, Bumblebee models does not have local
$U\left(1\right)$ gauge symmetry and expected not to have propagating
(massless) vector modes. Nonetheless, in these models massless modes
arise as Nambu-Goldstone (NG) modes which propagates \cite{Bluhm}. In the present work we bring together spontaneous LSB scenario with spontaneous global symmetry violation in order to see the cosmological implications of global monopoles on Bumblebee models.

Einstein's theory of general relativity, which is a metric theory
of gravitation \cite{Einstein:1916vd}, has successfully passed through
many experimental tests. One of the important testing technique is
a gravitational lensing which helps us to understand galaxies, dark
matter, dark energy and the universe \cite{Abbott:2016blz,Akiyama:2019cqa,Bartelmann:1999yn}.
This technique firstly was used by Eddington \cite{Dyson:1920cwa},
afterwards, various works on gravitational lensing have been done
for black holes, wormholes, global monopoles and other objects \cite{Virbhadra:1999nm,Virbhadra:2002ju,Virbhadra:2007kw,Virbhadra:2008ws,Keeton:1997by,Bozza:2002zj,Bozza:2009yw,Chen:2009eu,Eiroa:2002mk}.
There are many method to calculate gravitational lensing \cite{Sharif:2015qfa,Cao:2018lrd,Bisnovatyi-Kogan:2017kii,BisnovatyiKogan:2010ar,Cunha:2018acu}.
Recently, new method is derived by Gibbons and Werner which the deflection
angle of light can be calculated from non-rotating asymptotically
flat spacetimes using the Gauss-Bonnet theorem on the optical geometry
of the black hole \cite{Gibbons:2008rj}, then it is extended to stationary
spacetimes by Werner \cite{Werner:2012rc}. Since then, many works
have been done, one can see \cite{Crisnejo:2019ril}-\cite{Li:2020dln}.

The aim of the manuscript is to obtain a Schwarzschild like solution
with global monopole of Einstein equation in the presence of spontaneous
Lorentz symmetry breaking. We then study the effect of global monopoles
and spontaneous Lorentz symmetry breaking on the shadow of black hole
and also deflection of light. We also discuss the effect of global
monopoles on Lorentz symmetry breaking.

The manuscript is organized as follows: In section II, we derive the
Einstein fields equations for Einstein-Hilbert-Bumblebee gravity around
a global monopole fields. In section III, we obtain new Schwarzschild-like
black hole solution for Einstein-Hilbert-Bumblebee (EHB) gravity around
a global monopole. In section IV, we calculate the shadow of the black
hole. Section V is devoted to computation of the weak deflection angle
by Schwarzschild-like black hole solution for EHB gravity around a
global monopole using the GBT. We conclude our results in section
VI.

\section{EHB Gravity Around a Global Monopole}

In this part we review the EHB gravity \cite{Cas} whose Lagrangian
density is introduced as follows

\begin{align}
\mathcal{L}_{B} & =\sqrt{-g}\left(\frac{1}{2\kappa}R+\frac{\xi}{2\kappa}B^{\mu}B^{\nu}R_{\mu\nu}-\frac{1}{4}B_{\mu\nu}B^{\mu\nu}-V\left(B^{\mu}B_{\mu}\pm b^{2}\right)\right)+\mathcal{L}_{M},\label{Lag_Bumblebee}
\end{align}
where $B^{\mu}$ is the bumblebee field with field strength tensor
$B_{\mu\nu}=\partial_{\mu}B_{\nu}-\partial_{\nu}B_{\mu}$, $V\left(B^{\mu}B_{\mu}\pm b^{2}\right)$
being the potential which has terms responsible for the spontaneous
Lorentz symmetry breaking, $b^{2}$ is a real positive
constant and $\xi$ is the coupling constant of nonminimal gravity-bumblebee
interaction. $\mathcal{L}_{M}$ is the Lagrangian density of matter,
which in our case is the global monopole, and others field contents
with their couplings to the bumblebee field. Although,
the action (\ref{Lag_Bumblebee}) does not seem to be free from the
Ostrogradsky instabilities because of the coupling $B^{\mu}B^{\nu}R_{\mu\nu}$,
and is forbidden by gauge invariance in usual Einstein-Maxwell electrodynamics,
it is consistent in LSB scenarios with the axial gauge condition $b_{\mu}A^{\mu}=0$
(here we set the gauge potential $A^{\mu}$ instead of $B^{\mu}$)
\cite{Bluhm:2004ep,Kostelecky-0} where $b^{\mu}$ is the vacuum expectation
value (VEV) of $B^{\mu}$, i.e. $\left\langle B^{\mu}\right\rangle =b^{\mu}$,
in the Minkowski background spacetime geometry.
The equations of
motion of (\ref{Lag_Bumblebee}) is
\begin{align}
\mathcal{G}_{\mu\nu}= & \kappa\left(T_{\mu\nu}^{B}+T_{\mu\nu}^{M}\right)\label{EoM_1}
\end{align}
after varying (\ref{Lag_Bumblebee}) with respect to the metric $g_{\mu\nu}$.
We defined the Einstein tensor $\mathcal{G}_{\mu\nu}=R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R$
and energy-momentum tensor $T_{\mu\nu}=T_{\mu\nu}^{B}+T_{\mu\nu}^{M}$
where $T_{\mu\nu}^{B}$ is the contribution of the bumblebee field
to the energy-momentum tensor
\begin{eqnarray}
T_{\mu\nu}^{B}\equiv & -B_{\mu\sigma}B_{\phantom{\sigma}\nu}^{\sigma}-\frac{1}{4}g_{\mu\nu}B_{\alpha\beta}^{2}-g_{\mu\nu}V\left(B^{\mu}B_{\mu}\right)+4V^{\prime}B_{\mu}B_{\nu}+\frac{\xi}{\kappa}\left(\frac{1}{2}g_{\mu\nu}B^{\alpha}B^{\beta}R_{\alpha\beta}-B_{\nu}B^{\alpha}R_{\alpha\mu}-B_{\mu}B^{\alpha}R_{\alpha\nu}\right)\nonumber \\
 & +\frac{\xi}{\kappa}\left(\frac{1}{2}\nabla_{\alpha}\nabla_{\mu}\left(B^{\alpha}B_{\nu}\right)+\frac{1}{2}\nabla_{\alpha}\nabla_{\nu}\left(B_{\mu}B^{\alpha}\right)\right)+\frac{\xi}{\kappa}\left(-\frac{1}{2}\nabla^{\lambda}\nabla_{\lambda}\left(B_{\mu}B_{\nu}\right)-\frac{1}{2}g_{\mu\nu}\nabla_{\alpha}\nabla_{\beta}\left(B^{\alpha}B^{\beta}\right)\right),\label{T_mn^B}
\end{eqnarray}
and $T_{\mu\nu}^{M}$ is the matter sector of the energy-momentum
tensor which is defined as \cite{Barriola}
\begin{align}
T_{\mu}^{\left(M\right)\nu}= & \text{diag}\left(\frac{\eta^{2}}{r^{2}},\frac{\eta^{2}}{r^{2}},0,0\right)\label{T_mn^M}
\end{align}
where $\eta$ is the constant term which is related to the global
monopole charge. Note that the total energy-momentum tensor is covariantly
conserved:
\begin{equation}
\nabla^{\mu}T_{\mu\nu}=  0.
\end{equation}
Taking the variation of (\ref{Lag_Bumblebee}) with respect to the
bumblebee field $B_{\mu}$ provides the second equation of motion
\begin{equation}
\nabla^{\mu}B_{\mu\nu}=J_{\nu}\label{EOM_2}
\end{equation}
where $J_{\nu}=J_{\nu}^{B}+J_{\nu}^{M}$, with $J_{\nu}^{M}$ acting
as a source term for the bumblebee field and $J_{\nu}^{B}=2V^{\prime}B_{\nu}-\frac{\xi}{\kappa}B^{\mu}R_{\mu\nu}$
is the current due to self interaction of the bumblebee field.

The trace of (\ref{EoM_1}) is
\begin{align}
-\frac{1}{\kappa}R= & -4V\left(B^{\mu}B_{\mu}\right)+4V^{\prime}B_{\mu}B^{\mu}+\frac{\xi}{\kappa}\left(-\frac{1}{2}\nabla^{\lambda}\nabla_{\lambda}\left(B_{\mu}B^{\mu}\right)-\nabla_{\alpha}\nabla_{\beta}\left(B^{\alpha}B^{\beta}\right)\right)+T^{M}.\label{R}
\end{align}
Inserting the (\ref{R}) back into (\ref{EoM_1}) we get explicitly
\begin{align}
\frac{1}{\kappa}R_{\mu\nu}= & T_{\mu\nu}^{M}-\frac{1}{2}g_{\mu\nu}T^{M}-B_{\mu\sigma}B_{\phantom{\sigma}\nu}^{\sigma}-\frac{1}{4}g_{\mu\nu}B_{\alpha\beta}^{2}-g_{\mu\nu}V\left(B^{\mu}B_{\mu}\right)+4V^{\prime}B_{\mu}B_{\nu}+\frac{\xi}{\kappa}\left(\frac{1}{2}g_{\mu\nu}B^{\alpha}B^{\beta}R_{\alpha\beta}-B_{\nu}B^{\alpha}R_{\alpha\mu}-B_{\mu}B^{\alpha}R_{\alpha\nu}\right)\nonumber \\
 & +\frac{\xi}{\kappa}\left(\frac{1}{2}\nabla_{\alpha}\nabla_{\mu}\left(B^{\alpha}B_{\nu}\right)+\frac{1}{2}\nabla_{\alpha}\nabla_{\nu}\left(B_{\mu}B^{\alpha}\right)\right)+\frac{\xi}{\kappa}\left(-\frac{1}{2}\nabla^{\lambda}\nabla_{\lambda}\left(B_{\mu}B_{\nu}\right)-\frac{1}{2}g_{\mu\nu}\nabla_{\alpha}\nabla_{\beta}\left(B^{\alpha}B^{\beta}\right)\right)\nonumber \\
 & +\frac{1}{2}g_{\mu\nu}\left(4V\left(B^{\alpha}B_{\alpha}\right)-4V^{\prime}B^{\alpha}B_{\alpha}\right)-\frac{1}{2}g_{\mu\nu}\frac{\xi}{\kappa}\left(-\frac{1}{2}\nabla^{\lambda}\nabla_{\lambda}\left(B^{\alpha}B_{\alpha}\right)-\nabla_{\alpha}\nabla_{\beta}\left(B^{\alpha}B^{\beta}\right)\right)\label{R_mn}
\end{align}

The potential $V\left(B_{\mu}B^{\mu}\pm b^{2}\right)$ is chosen in
a way that the vacuum expectation value for $B_{\mu}$ has to be nonvanishing
in order to have spontaneous Lorentz symmetry breaking. Because of
this reason, the general form of the potential, $V\left(B_{\mu}B^{\mu}\pm b^{2}\right)$
is set to zero to determine the VEV of the bumblebee field which gives
the following condition
\begin{align}
B_{\mu}B^{\mu}\pm b^{2}= & 0.\label{Condition}
\end{align}
The solution of (\ref{Condition}) has a nonnull vacuum expectation
value $\left\langle B^{\mu}\right\rangle =b^{\mu}$ which breaks the
Lorentz symmetry \cite{Cas}.

Note that Maxwell's electrodynamics in the non-linear gauge $A_\mu A_\mu-b^2 = 0$ and the bumblebee model with solutions confined to the case of $B_\mu B_\mu -b^2 = 0$ have same structure. However, in Maxwell's electrodynamics, the particles that carry that force, called photons, is understood by gauge symmetry, but in the bumblebee model is obtained from the nature of Goldstone bosons appearing from a spontaneous symmetry breaking of Lorentz invariance \cite{Escobar:2017fdi}.

\section{The Schwarzschild-like black hole of EHB Gravity Around Global Monopole}

In this part a static spherically symmetric solution to the Einstein
equations is obtained. We take the Birkhoff metric as an ansatz
\begin{align}
g_{\mu\nu}= & \text{diag}\left(-e^{2\gamma},e^{2\rho},r^{2},r^{2}\sin^{2}\theta\right),\label{Bhirkoff}
\end{align}
where $\gamma$ and $\rho$ are functions of $r$, and fix the Bumblebee
field in its vacuum expectation value \cite{Bertolami:2005}

\begin{align}
B_{\mu}= & b_{\mu}.\label{B_equal_b}
\end{align}
Since the potential can be choosen simply as $V\left(x\right)=\frac{1}{2}\lambda x^{2}$
where $\lambda$ is a real coupling constant or $V\left(x\right)=\lambda x$
and as long as (\ref{Condition}) and (\ref{B_equal_b}) holds for
both choices of potentials one has \cite{Kostelecky-0}
\begin{align}
V= & 0,\quad V^{\prime}=0.\label{potential_0}
\end{align}
Also we take
\begin{equation}
b_{\mu}=\left(0,b_{r}\left(r\right),0,0\right)\label{b_m}
\end{equation}
for which the field strength vanishes, $b_{\mu\nu}=0$. Although,
the ansatz (\ref{b_m}) can be generalized for $b_{t}\ne0$ (i.e.,
$b_{t}=\text{constant}$) for simplicity we keep $b_{t}=0$. Note that setting $B_t=0$ indicates that the vector field can diverge at the event horizon. One can also introduce $B_t=q=constant$, which still gives $B_{\mu \nu}=0$.  The advantage of such generalized solution is that the vector field is regular either the future or past event horizon \cite{Heisenberg:2017hwb}. Moreover, the case of $B^{\mu} B_{\mu}\neq0$ is also interesting, and need to be studied separately. These cases will be studied in our future projects. The condition $b^{\mu}b_{\mu}=b^{2}=\text{constant}$ gives the explicit
form of the radial background field
\begin{align}
b_{r}\left(r\right)= & \left|b\right|e^{\rho}.\label{b_r}
\end{align}
Then, (\ref{R_mn}) can be written as following
\begin{align}
0= & \bar{R}_{\mu\nu}=R_{\mu\nu}-\kappa\left(T_{\mu\nu}^{M}-\frac{1}{2}g_{\mu\nu}T^{M}\right)-\frac{\xi}{2}g_{\mu\nu}b^{\alpha}b^{\beta}R_{\alpha\beta}+\xi b_{\nu}b^{\alpha}R_{\alpha\mu}+\xi b_{\mu}b^{\alpha}R_{\alpha\nu}-\frac{\xi}{2}\nabla_{\alpha}\nabla_{\mu}\left(b^{\alpha}b_{\nu}\right)-\frac{\xi}{2}\nabla_{\alpha}\nabla_{\nu}\left(b_{\mu}b^{\alpha}\right)\nonumber \\
 & +\frac{\xi}{2}\nabla^{\lambda}\nabla_{\lambda}\left(b_{\mu}b_{\nu}\right).\label{Einstein_eqns}
\end{align}
where the trace of the energy-momentum tensor is \cite{Barriola}
\begin{align}
T^{M}= & 2\frac{\eta^{2}}{r^{2}}.\label{Trace_of_T_mn}
\end{align}
The combination constructed from the energy-momentum tensor and its
trace in (\ref{Einstein_eqns}) reads
\begin{align}
T_{\mu\nu}^{M}-\frac{1}{2}g_{\mu\nu}T^{M}= & \left(0,0,-\eta^{2},-\eta^{2}\text{Sin}^{2}\left(\theta\right)\right),\label{T_mn_T}
\end{align}
and the components of the Ricci tensor in (\ref{Einstein_eqns}) are
\begin{align}
R_{tt}= & e^{2\left(\gamma-\rho\right)}\left[\partial_{r}^{2}\gamma+\left(\partial_{r}\gamma\right)^{2}-\partial_{r}\gamma\partial_{r}\rho+\frac{2}{r}\partial_{r}\gamma\right],\label{R_tt}\\
R_{rr}= & -\partial_{r}^{2}\gamma-\left(\partial_{r}\gamma\right)^{2}+\partial_{r}\gamma\partial_{r}\rho+\frac{2}{r}\partial_{r}\rho,\label{R_rr}\\
R_{\theta\theta}= & e^{-2\rho}\left[r\left(\partial_{r}\rho-\partial_{r}\gamma\right)-1\right]+1.\label{R_theta}
\end{align}
The components of (\ref{Einstein_eqns}) become
\begin{align}
\bar{R}_{tt}= & \left(1+\frac{\ell}{2}\right)R_{tt}+\frac{\ell}{r}\left(\partial_{r}\rho+\partial_{r}\gamma\right)e^{2\left(\gamma-\rho\right)},\label{barR_tt}\\
\bar{R}_{rr}= & \left(1+\frac{3\ell}{2}\right)R_{rr},\label{barR_rr}\\
\bar{R}_{\theta\theta}= & \left(1+\ell\right)R_{\theta\theta}-\ell\left(\frac{1}{2}r^{2}e^{-2\rho}R_{rr}+1\right)+\eta^{2},\label{barR_theta}\\
\bar{R}_{\phi\phi}= & \sin^{2}\left(\theta\right)\bar{R}_{\theta\theta},\label{barR_phi}
\end{align}
where $\ell=\xi b^{2}$. These equations (\ref{barR_tt},\ref{barR_rr},\ref{barR_theta},\ref{barR_phi})
are indipendently equal to zero. Therefore, the following combination
can be written to find the function $\rho\left(r\right)$ \cite{Cas}
\begin{align}
r^{2}e^{-2\rho}\bar{R}_{tt}+r^{2}e^{-2\rho}\bar{R}_{rr}+2\bar{R}_{\theta\theta}= & 0,\label{first_comb}
\end{align}
which yields
\begin{align}
e^{2\rho}= & \left(1+\ell\right)\left(1+\eta^{2}-\frac{\rho_{0}}{r}\right)^{-1}.\label{rho_func}
\end{align}
In order to find the function $\gamma\left(r\right)$ the following
second combination is constructed \cite{Cas} from (\ref{barR_tt},\ref{barR_rr},\ref{barR_theta},\ref{barR_phi})
which is
\begin{align}
r^{2}e^{-2\gamma}\bar{R}_{tt}-\left(1+\frac{2}{\ell}\right)\bar{R}_{\theta\theta}= & 0.\label{second_comb}
\end{align}
After a straightforward calculation one reach the following function
\begin{align}
e^{2\gamma}= & 1+\eta^{2}-\frac{\rho_{0}}{r}.\label{gamma_func}
\end{align}
Then the Lorentz symmetry breaking spherically symmetric solution
for EHB can be written as
\begin{align}
ds^{2}= & -\left(1-\bar{\mu}-\frac{2M}{r}\right)dt^{2}+\left(1+\ell\right)\left(1-\bar{\mu}-\frac{2M}{r}\right)^{-1}dr^{2}+r^{2}d\theta^{2}+r^{2}\sin^{2}\theta\,d\phi^{2}\label{solution}
\end{align}
where we have defined $\rho_{0}=2M$ and the global monopole term
$\bar{\mu}$ which is defined as $\bar{\mu}=-\eta^{2}$. The metric
(\ref{solution}) recovers LSB spherically symmetric solution when
$\eta=0$ \cite{Cas} and the usual Schwarzschild metric for limit
$\ell\rightarrow0$.

Then we introduce the following coordinate transformation: $r\rightarrow\left(1-\bar{\mu}\right)^{-1/2}r,t\rightarrow\left(1-\bar{\mu}\right)^{1/2}t,M\rightarrow\left(1-\bar{\mu}\right)^{-3/2}M$:
The spacetime metric of the Lorentz symmetry breaking spherically
symmetric solution for EHB becomes:
\begin{align}
ds^{2}= & -\left(1-\frac{2M}{r}\right)dt^{2}+\left(1+\ell\right)\left(1-\frac{2M}{r}\right)^{-1}dr^{2}+g^{2}r^{2}\left(d\theta^{2}+\sin^{2}\theta\,d\phi^{2}\right)\label{solution}
\end{align}
where $g^{2}=1-\bar{\mu}$.

The event horizon of the black hole locates at $g_{tt}(r_{h})=0$
so that $r_{h}=2M$, which does not depend on $\ell$ and $g$. It
means that there is not any effect on event horizon by bumblebee field
and global monopole field. On the other hand, Kretschmann invariant
is calculated as:

\begin{equation}
K_{\text{Kretschmann}}=R_{\alpha\beta\mu\nu}R^{\alpha\beta\mu\nu}={\frac{4\,\left({g}^{2}-\ell-1\right)^{2}{r}^{2}-16\,M{g}^{2}\left({g}^{2}-\ell-1\right)r+48\,{M}^{2}{g}^{4}}{{r}^{6}{g}^{4}\left(1+\ell\right)^{2}}},\label{KK}
\end{equation}
note that there is a physical singularity at $r=0$, because
the Kretschmann invariant is divergent.
The Eq. \ref{KK} is different than the Schwarzschild case, which
means that the Eq. \ref{solution} is a real solution containing Lorentz-violating
corrections, because it is impossible to find a coordinate transformation
between the Eq. \ref{solution} and the Schwarzschild case. Moreover,
for $r_{h}=2M$ the Kretschmann scalar is finite therefore such a
singularity at the event horizon can be removed by means of a coordinate
transformation. The Hawking-Bekenstein temperature of the black hole
is \cite{Kanzi:2019gtu}
\begin{equation}
T_{H}=\frac{\kappa}{2\pi}=\left.\frac{1}{4\pi\sqrt{-g_{tt}g_{rr}}}\frac{dg_{tt}}{dr}\right|_{r=r_{h}}=\left.\frac{1}{2\pi\sqrt{1+\ell}}\frac{M}{r^{2}}\right|_{r=r_{h}}=\frac{1}{8\pi M\sqrt{1+\ell}}
\end{equation}
where the surface gravity $\kappa=\nabla_{\mu}\chi^{\mu}\nabla_{\nu}\chi^{\nu}$
with Killing vector field $\chi^{\mu}$ and $k^{2}=-\frac{1}{4}g^{tt}g^{ab}g_{tt,a}g_{tt,b}$
is used. It is clear that the increasing LSB parameter $\ell$
reduces the temperature of the black hole and temperature does not
depend on the global monopole parameter $g$.

\section{Shadow of the Schwarzschild Like Solution with Global Monopole in
EHB Gravity}

Here, we investigate the shadow radius of the Schwarzschild like solution
with global monopole in EHB gravity. The Lagrangian $\mathcal{L}(x,\dot{x})=(1/2)g_{\mu\nu}\dot{x}^{\mu}\dot{x}^{\nu}$
for the geodesics of spherically symmetric and static spacetime metric
is
\begin{equation}
\begin{aligned}\mathcal{L}(x,\dot{x})=\frac{1}{2}\left(-f(r)\dot{t}^{2}+\frac{(1+\ell)}{f(r)}\dot{r}^{2}+g^{2}r^{2}\left(\dot{\theta}^{2}+\sin^{2}\theta\dot{\phi}^{2}\right)\right)\end{aligned}
\end{equation}
where $f(r)=1-\frac{2M}{r}$.

Using the Euler-Lagrange equation $\frac{d}{d\lambda}\left(\frac{\partial\mathcal{L}}{\partial\dot{x}^{\mu}}\right)-\frac{\partial\mathcal{L}}{\partial x^{\mu}}=0$
within equatorial plane, ($\theta=\pi/2)$, the two conserved quantities
such as energy and angular momentum are obtained as

\begin{equation}
E=f(r)\dot{t},\quad L=g^{2}r^{2}\dot{\phi}.
\end{equation}

To obtain the geodesics equation for light, we write

\begin{equation}
0=-f(r)\dot{t}^{2}+\frac{(1+\ell)}{f(r)}\dot{r}^{2}+g^{2}r^{2}\dot{\phi}^{2}.
\end{equation}
Then using the conserved quantities $E$ and $L$ in to the above
equation, we find the orbit equation for photon as follows:

\begin{equation}
\left(\frac{dr}{d\phi}\right)^{2}=\frac{g^{2}r^{2}f(r)}{(1+\ell)}\left(\frac{g^{2}r^{2}}{f(r)}\frac{E^{2}}{L^{2}}-1\right),\label{eff}
\end{equation}
one can write it in the form of effective potential
\begin{equation}
\left(\frac{dr}{d\phi}\right)^{2}=V_{eff}
\end{equation}

with
\begin{equation}
V_{eff}=\frac{g^{4}r^{4}}{(1+\ell)}\left(\frac{E^{2}}{L^{2}}-\frac{f(r)}{g^{2}r^{2}}\right).
\end{equation}

The orbit equation depends only on the impact parameter $b=L/E$.
At the turning point of the trajectory $r=r_{ph}$, the condition
must satisfy $dr/\left.d\phi\right|_{r_{ph}}=0$ or $V_{eff}=0,\quad V_{eff}^{\prime}=0$
\cite{synge,Luminet:1979nyg}. The impact parameter at turning point
is

\begin{equation}
\frac{1}{b^{2}}=\frac{f(r_{ph})}{g^{2}r_{ph}^{2}}\label{impact}
\end{equation}

and using the conditions of $dr/\left.d\phi\right|_{r_{ph}}=0$ and
$d^{2}r/d\phi^{2}|_{r_{ph}}=0$, one can find the radius of the photon
sphere $r_{ph}$ by solving this equation:
\begin{equation}
0=\frac{d}{dr}B(r)^{2}
\end{equation}
\begin{equation}
\frac{f^{\prime}\left(r_{ph}\right)}{f\left(r_{ph}\right)}-\frac{h^{\prime}\left(r_{ph}\right)}{h\left(r_{ph}\right)}=0.\label{photon}
\end{equation}
where $B^{2}(r)=\frac{h(r)}{f(r)}$ and $h(r)=g^{2}r^{2}$. Hence,
the analysis of Eq. \ref{impact} and Eq. \ref{photon} show that
the position of the photon sphere is $r_{ph}=3M$ and the critical
impact factor is $b_{crit}=3\sqrt{3}gM$.

In spherical symmetric spacetime, the black hole shadow is obtained
by using the light rings. The light rings corresponds to a critical
point of Eq. \ref{photon}. The Eq. \ref{eff} becomes
\begin{equation}
\left(\frac{dr}{d\phi}\right)^{2}=\frac{h(r)f(r)}{1+\ell}\left(\frac{B^{2}(r)}{B^{2}(r_{ph})}-1\right).
\end{equation}
To calculate shadow radius, we use the angle $\alpha$ between the
light ray and radial direction as follows \cite{Perlick:2021aok}:
\begin{equation}
\cot\alpha=\left.\frac{\sqrt{(1+\ell)}}{\sqrt{f(r)h(r)}}\frac{dr}{d\phi}\right|_{r=r_{0}}.
\end{equation}
and
\begin{equation}
\cot^{2}\alpha=\frac{B^{2}\left(r_{0}\right)}{B^{2}(r_{ph})}-1
\end{equation}
Using the relation $\sin^{2}\alpha=\frac{1}{1+\cot^{2}\alpha}$, we
obtain
\begin{equation}
\sin^{2}\alpha=\frac{B^{2}(r_{ph})^ {}}{B^{2}\left(r_{0}\right)^ {}}.
\end{equation}
Since the critical value of impact parameter is related with radius
of photon sphere $b_{cr}=B(r_{ph})$, then the shadow is obtained
as

\begin{equation}
\sin^{2}\alpha_{\mathrm{sh}}=\frac{b_{\mathrm{cr}}^{2}}{B\left(r_{0}\right)^{2}}.
\end{equation}

Then the shadow radius of the black hole for a static observer $r_{0}$
is \cite{Konoplya:2019sns}
\begin{equation}
R_{s}=r_{0}\sin\alpha=\sqrt{\frac{h(r_{ph})f\left(r_{0}\right)}{f\left(r_{ph}\right)}}
\end{equation}
and for a static observer at large distance is
\begin{equation}
R_{s}^{2}=\frac{g^{2}r_{ph}^{2}}{f\left(r_{ph}\right)}.
\end{equation}
The apparent shape of the shadow can be found by a stereographic projection
in terms of celestial coordinates X and Y which as
\begin{equation}
\begin{gathered}X=\lim_{r_{0}\longrightarrow\infty}\left(-\left.r_{0}^{2}\sin\theta_{0}\frac{d\phi}{dr}\right|_{\left(r_{0},\theta_{0}\right)}\right)\\
Y=\lim_{r_{0}\longrightarrow\infty}\left(\left.r_{0}^{2}\frac{d\theta}{dr}\right|_{\left(r_{0},\theta_{0}\right)}\right).
\end{gathered}
\end{equation}

\begin{figure}[ht!]
\centering \includegraphics[scale=0.6]{shadow1} \caption{Shadow radius for Schwarzschild Like Solution with Global
Monopole in Bumblebee Gravity, $g=1$ Schwarzschild (black), $g=0.4$
(orange), $g=0.5$ (blue), $g=0.6$ (green), $g=0.7$ (red), $g=0.8$
(purple), and $g=0.9$ (gray) at $M=1$.}
\label{shadow}
\end{figure}

Here, we shall use the  reported angular size of the black hole shadow in the M87$^*$ galactic center reported by  EHT  $\theta_s = (42 \pm 3)\mu as$, along with the distance to M87$^*$ given by  $D = 16.8 $ Mpc, and the mass of M87$^*$ central object $M = 6.5 \times 10^9$ M\textsubscript{\(\odot\)} to constrain the mass around the black hole M87$^*$. The diameter of the shadow in units of mass $d_{M87^*}$ is given by \cite{Allahyari:2019jqz}
\begin{eqnarray}
d_{M87^*}=\frac{D \,\theta_s}{M_{87^*}}=11.0 \pm 1.5,
\end{eqnarray}
where $d_{M87^*}=2 R_{M87^*}$. The observable quantity such as the angular diameter of the
M87$^*$  BH can be estimated using the observable $R_{M87^*}$
as follows $\theta_{s}=2 R_{M87^*} M_{M87^*} / D$.
The radius of the observed shadow of the M87$^*$ in unit mass is

\begin{eqnarray}
 R_{M87^*} = 5.5 \pm 0.75.
\end{eqnarray}
Shadow radius of the Schwarzschild-like black hole with a topological defect in bumblebee gravity  where the global monopole parameter is $\bar{\mu}\simeq10^{-5}$
\cite{Vilenkin:2000jqa} is
\begin{eqnarray}
 R_{s} = 5.19613.
\end{eqnarray}
It is clear that Schwarzschild-like black hole with a topological defect in bumblebee gravity's shadow can appear up to $5.5\%$ smaller than it would in a  case of Schwarzschild-like black hole, providing a clear way to test topological defect.

In the Table.\ref{tab:table1}, we provide the shadow radius of the M87$^*$ as compared with Schwarzschild-like black hole with a topological defect in bumblebee gravity.
\begin{table}[ht!]
    \centering
    \begin{tabular}{ |p{2cm}|p{2cm}|p{2cm}|p{2cm}|p{2cm}|  }
    \hline
        $g$ & $R_s$ \\ [1 ex]
        \hline
         $0.4 $ & $2.07846$ \\
        \hline
        $0.5 $ & $2.59808$ \\
        \hline
        $0.6$ & $3.11769$  \\
        \hline
        $0.7 $ & $3.63731$ \\
        \hline
        $1 $ & $5.19615$  \\
        \hline
    \end{tabular}
    \caption{Effect of the topological defects on the shadow size for the observed M87$^*$.}
    \label{tab:table1}
\end{table}

The shadow radius of the black hole increasing with the increasing
value of global monopole parameter $g$ as shown in Fig. \ref{shadow}.
On the other hand, the shadow radius does not depend on the LSB parameter
$\ell$. The relation between the high energy absorption cross section
and the shadow for the observer located at infinity is given by the
energy emission rate of the black hole as follows \cite{Decanini:2011xw,Wei:2013kza}:
\begin{equation}
\dfrac{d^{2}E(\omega)}{d\omega dt}=\dfrac{2\pi^{3}R_{s}^{2}}{e^{\omega/T}-1}\omega^{3},
\end{equation}

The plots in Fig. \ref{emg} and Fig. \ref{eml} shows the variation
of energy emission rate for frequency $\omega$ in different values
of the global monopole parameter $g$ and LSB parameter $\ell$, respectively.

\begin{figure}[ht!]
\centering \includegraphics[scale=0.6]{emg} \caption{The BH emission rate for different values of magnetic monopole term
$g$ at $M=1$ and $\ell=0.9$.}
\label{emg}
\end{figure}

\begin{figure}[ht!]
\centering \includegraphics[scale=0.6]{eml} \caption{The BH emission rate for different values of LSB parameter $\ell$
at $M=1$ and $g=0.5$.}
\label{eml}
\end{figure}

\section{Weak deflection angle of Schwarzschild Like Solution with Global
Monopole in EHB Gravity}

To obtain the weak deflection angle of Schwarzschild Like Solution
with Global Monopole in Bumblebee Gravity, we write the metric in
the optical form within equatorial plane $\theta=\pi/2$, and obtain
null geodesics ($\mathrm{d}s^{2}=0$):
\begin{eqnarray}
\mathrm{d}t^{2}=\frac{(1+\ell)\mathrm{d}r^{2}}{f(r)^{2}}+\frac{g^{2}r^{2}\mathrm{d}\phi^{2}}{f(r)},\label{metric2}
\end{eqnarray}
where $f(r)=1-\frac{2M}{r}$.

Afterwards, we calculate the Gaussian optical curvature $K$ in 2-dimensions
for the above space, which gives an intrinsic property of the space:
\begin{equation}
K=\frac{R_{icciScalar}}{2}\approx-2\,{\frac{M}{{r}^{3}}}+2\,{\frac{Ml}{{r}^{3}}}-2\,{\frac{M{l}^{2}}{{r}^{3}}}.\label{curvature}
\end{equation}
Note, that the Gaussian optical curvature is found as negative in
leading order terms, which imply that all the light rays locally diverge.
Hence, after converging, to obtain the multiple images, we will use
the Gauss-Bonnet theorem for the region  $S_{R}$ in manifold
shown in Fig. \ref{f1}, with boundary of circular curve $\gamma_{R}$
and geodesic curve $\gamma_{\bar{g}}$ as

$\partial S_{R}=\gamma_{\bar{g}}\cup\gamma_{R}$ \cite{Gibbons:2008rj}
\begin{equation}
\iint\limits _{S_{R}}K\,\mathrm{d}S+\oint\limits _{\partial S_{R}}\bar{\kappa}\,\mathrm{d}t=2\pi\chi(S_{R})-(\theta_{O}+\theta_{S})=\pi.\label{gaussbonnet}
\end{equation}

where the $\bar{\kappa}$ stands for the geodesics curvature. Moreover,
$\theta_{O}+\theta_{S}\to\pi$ implies that jump angles become $\pi/2$
when $R$ going to infinity. Also one can say that $S_{R}$ is non-singular
region, so that the Euler characteristic is $\chi(S_{R})=1$. Then,
$\bar{\kappa}(\gamma_{\tilde{g}})=0$. In addition, the near asymptotic
limit of $R$, $\gamma_{R}:=r(\varphi)=R=const.$, one can write the
radial component of the geodesic curvature as follows: \cite{Gibbons:2008rj}

\begin{equation}
\bar{\kappa}(\gamma_{R})=\left|\nabla_{\dot{\gamma}_{R}}\dot{\gamma}_{R}\right|=\left(\tilde{g}_{rr}\dot{\gamma}_{R}^{r}\dot{\gamma}_{R}^{r}\right)^{\frac{1}{2}}\to\frac{1}{R}.
\end{equation}

\begin{figure}[h!]
\center \includegraphics[width=0.5\textwidth]{figg} \caption{ Here, the integration domain $S_{R}$, namely the equatorial
plane $(r,\varphi)$, in which $\alpha$ is the total deflection angle
and $u$ is the impact parameter.}
\label{f1}
\end{figure}

After substitute this result, yielding: $\bar{\kappa}(\gamma_{R})\mathrm{d}t=\frac{g}{\sqrt{(1+\ell)}}\,\mathrm{d}\,\varphi$.
Using the straight line approximation for the weak field regions,
$r_{s}=u/\sin\varphi$ at zeroth-order, where $u$ is the impact parameter.
Then the Gauss-Bonnet equation becomes:
\begin{eqnarray}
\pi=\int\limits _{0}^{\pi}\int\limits _{\frac{u}{\sin\varphi}}^{\infty}K\,\mathrm{d}S+\frac{g}{\sqrt{(1+\ell)}}\int\limits _{0}^{\pi+\alpha}\mathrm{d}\varphi,\label{def1}
\end{eqnarray}
where optical surface area is defined as $\mathrm{d}S=r\mathrm{d}r\,\mathrm{d}\varphi$,
and $\alpha$ is a deflection angle.

Afterwards, the optical geometry \eqref{curvature} within the Gauss-Bonnet
theorem \eqref{def1}, give us the weak deflection angle:
\begin{equation}
\alpha=\frac{\sqrt{(1+\ell)}\pi}{g}-\pi-\sqrt{(1+\ell)}\int\limits _{0}^{\pi}\int\limits _{\frac{u}{\sin\varphi}}^{\infty}K\,r\,\mathrm{d}r\,\mathrm{d}\varphi.\label{angle}
\end{equation}

Hence, the weak deflection angle $\alpha$ of Schwarzschild Like Solution
with Global Monopole in Bumblebee Gravity in weak field limits is
found as follows:
\begin{equation}
\alpha\simeq4\,{\frac{M}{u}}+\,\frac{\ell\pi}{2}+2\,{\frac{M\ell}{u}}+\,\frac{\bar{\mu}\pi}{2}.\label{deflection}
\end{equation}

Note that the bumblebee parameter $\ell$, the mass term and the global
monopole term $\bar{\mu}$ all of them increase the deflection angle
as shown in Fig. \ref{def1} and Fig. \ref{def2}. The expression
of weak deflection angle is consistent with \cite{Li:2020dln} when
global monopole term $\bar{\mu}=0$. When the bumblebee parameter
$\ell=0$, the effect of global monopole fields on the deflection
angle in Eq. \ref{deflection} for comparison with other type of defects,
e.g., cosmic strings show that the increased value of the deflection
angle is too small, $\alpha\simeq\frac{4M}{b}+4\pi\nu$ \cite{Ovgun:2019wej}
with the order of 10 arcsec, (for cosmic string parameter $\nu\simeq10^{-6}$)
where the global monopole parameter is $\bar{\mu}\simeq10^{-5}$
\cite{Vilenkin:2000jqa}. Moreover, a  gravitating global monopole ($M \approx 0$)
deflects light although there is no gravity as $\alpha \simeq\,\,\frac{\ell\pi}{2}+\,\frac{\bar{\mu}\pi}{2} $.

\begin{figure}[ht!]
\centering \includegraphics[scale=0.6]{def} \caption{Weak deflection angle $\alpha$ versus impact parameter $u$ of Schwarzschild
Like Solution with Global Monopole in Bumblebee Gravity, for different
values of monopole parameter $\bar{\mu}$ at $M=1$ and $\ell=0.5$.}
\label{def1}
\end{figure}

\begin{figure}[ht!]
\centering \includegraphics[scale=0.6]{def2} \caption{Weak deflection angle $\alpha$ versus impact parameter $u$ of Schwarzschild
Like Solution with Global Monopole in Bumblebee Gravity, for different
values of LSB parameter $\ell$ at $M=1$ and $\bar{\mu}=0.5$.}
\label{def2}
\end{figure}

\section{Conclusions}

We have investigated a static spherically symmetric vacuum solution
for the EHB gravity in the presence of a global monopole. We have
obtained a spherically symmetric solution similar to the Schwarzschild
black hole. This solution reduces to spherically symmetric solution
in the LSB scenario when $\bar{\mu}=0$. Moreover, we have shown the
effect of the global monopole term on the shadow of the black hole
as well as the energy emission rate. The shadow radius of the black
hole increasing with the increasing value of global monopole parameter
$g$ as shown in Fig. \ref{shadow}. On the other hand, the shadow
radius does not depend on the LSB parameter $\ell$. Furthermore,
we have also calculated the deflection angle of the light in this
geometry by using the GBT. It is found that both the bumblebee parameter
and the global monopole term increases the deflection angle. If the
global monopole term is set to $\bar{\mu}=-\ell$ then part of the
effect of the bumblebee parameter on the deflection angle cancel out in leading order terms.
However, the bumblebee parameter still gives a correction to the deflection
angle. In addition to this, setting $\bar{\mu}=-\ell(1+{\frac{4M}{u\pi}})$
directly remove the effect of the bumblebee parameter on the deflection
angle.

Note that our calculations was done in the weak-field limit, one can study the strong gravitational lensing to see other contributions.

In summary, we see that the global monopole term with the LSB parameter can be  altered the shadow of the black hole as well as the weak deflection angle.

The effect of the topological defects within the bumblebee gravity on the shadow radius has obtained for the first time in the literature here. We have showed that Schwarzschild-like black hole with a topological defect in bumblebee gravity's shadow can appear up to $5.5\%$ smaller than it would in a  case of Schwarzschild-like black hole, providing a clear way to test topological defect. While the current shadow image of black hole $M87^*$ is too fuzzy to tell the difference, efforts are underway to take even better pictures of more black holes, probing some of the deepest mysteries of the universe in the process.

We end with some comments on future studies from several perspectives, which we did not address in this paper. We can extend the analysis for the generalized ansatz $b_{t}$ in Eq. \ref{b_m} can be generalized for  example $b_{t}=\text{constant}$. Second, One can also introduce $B_t=q=constant$  or $B^{\mu} B_{\mu}\neq0$ and try to find new black hole solutions. On the other hand, one can generalize EHB gravity to vector-tensor theories and so it will be of interest to study what happens in the presence of vector-tensor fields within the LSB parameter. We will leave these interesting things for future works.

\begin{acknowledgments}
The authors are grateful to the anonymous referees for their valuable comments and suggestions to
improve the paper.
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


Kubernetes (K8s) is an operating system level utility that allows you to access your programs, allows your programs to talk to each other, and generally keeps them running.
A Kubernetes consultant learns your expectations of what your organization should do and then sets up your Kubernetes cloud space to manage your business programs. Through powerful container programming, similar to that used by Google, Kubernetes, or Kube as it is sometimes affectionately known, a Kubernetes consulting specialist can set your programs up in clusters that perform similar or related functions – such as the way daily attendance will affect the meals prepared for lunch in a large school.
Because your business programs are talking to each other, small bits of data that are entered through invoices or receipts, appointment calendars or meeting minutes, make their way not into just one function, but into all functions that might be affected by the information. Furthermore, it can be set up to do it without a great deal of added effort on your part.
Imagine running a table at a flea market and using your cell phone to record sales. Information about each sale is uploaded to your cloud as it occurs. No more wearisome tallying up at the end of the day, no more chasing pennies through several columns of spreadsheets to learn where the balance is off. The information is entered and simultaneously sent to all the other places where it might need to go. Setting containers up in clusters greatly facilitates the speed and efficiency with which the various functions interact. That's progress.
Where do Kubernetes consulting specialists come in? They can set up your Kubernetes cloud – you would probably expect that. But they can go a step or two farther and help educate you and your staff so that you understand what your containers are doing. While Kubernetes greatly improves efficiency and cuts down on errors because information is entered once and duplicated digitally, human error is always possible.
Of course, Kubernetes consultants will be around to help out by tracking any of the few problems that might develop, but it is always good for you and your staff to have a list of simple, first things to try if a problem should arise. Or to put it another way: Kubernetes is a solid, reliable platform that will behave in expected ways. They are your backup for when the unexpected occurs.


text:
Newborn girl left at Coral Springs fire station is in good health
Home » Newborn girl left at Coral Springs fire station is in good health
BY LIDIA DINKOVA
ldinkova@MiamiHerald.com
When Coral Springs firefighters heard the alarm Monday night, it wasn't a siren but a baby's cry.
Outside the fire station at 4550 Rock Island Rd. they found a newborn girl.
"She was wrapped in some T-shirts," said Mike Moser, spokesman for the Coral Springs Fire Department.
"The child still had the umbilical cord and some of the placenta attached."
Firefighters took the baby to Northwest Medical Center, where doctors said she was in good condition.
Then, she was taken to A Safe Haven for Newborns, a state organization that works with private adoption agencies, Moser said.
This was the second baby in about three years to be dropped off at the Coral Springs Fire Department, and the 159th in Florida to be left with A Safe Haven for Newborns since 2000.
The number of babies left at Safe Havens reached all-time highs in 2005 and 2007 when 23 babies were left at fire stations or hospitals.
But the number has steadily decreased over the past four years. So far this year, eight babies have been left at Florida Safe Havens.
Florida's Safe Haven for Newborns Act, passed in 2000, allows mothers to drop off babies one week or younger at any hospital, fire station or emergency medical services station, anonymously, without consequences.
"All these babies get adopted," said Nick Silverio, founder of A Safe Haven for Newborns. "They have a future. They could be the next president. They could be a Supreme Court justice. But more importantly, they will have a mom and dad."
Newborn girl left at Coral Springs fire station is in good health2011-06-272016-12-27https://asafehavenfornewborns.com/wp-content/uploads/2017/01/asafehavenfornewbornsh.jpgA Safe Haven for Newborns | Pregnant Need Help?https://asafehavenfornewborns.com/wp-content/uploads/2017/01/asafehavenfornewbornsh.jpg200px200px
A healthy newborn girl was left at a Fire Rescue station in Florida.News
Baby in good condition after being left at fire stationNews


text:
Die Gemeinde Šavnik () ist eine Gemeinde in Montenegro. Der Verwaltungssitz ist der Hauptort Šavnik.

Zur Gemeinde gehören 27 Siedlungen, von denen Šavnik die größte ist. Die Gemeinde leidet unter starkem Bevölkerungsverlust und ist die montenegrinische Gemeinde mit der geringsten Einwohnerzahl.

Geografie
Šavnik befindet sich am Zusammenfluss von drei Flüssen – Bukovica, Bijela und Šavnik, auf einer Höhe von 840 Metern. Die Gemeinde befindet sich in der nordwestlichen Region von Montenegro in der Region Drobnjaci, benannt nach dem lokalen Clan der Drobnjaci. Šavnik liegt an einer Regionalstraße zwischen Nikšić (45 km) und Žabljak (15 km).

Bevölkerung
Die Gemeinde Šavnik hat 2070 Einwohner. Die Gemeinde ist ethnisch gemischt. Laut der Volkszählung 2011 bestand die Bevölkerung aus Montenegrinern (58,94 %) und Serben (30 %). Beim Unabhängigkeitsreferendum 2006 entschieden sich ca. 57 Prozent der Einwohner gegen die Unabhängigkeit.

Einzelnachweise

Savnik


text:
Minuci Acilià (llatí: Minucius Acilianus) va ser un magistrat romà, amic de Plini el jove.

Va exercir diverses magistratures: la de qüestor, la de tribú de la plebs i la de pretor, totes elles sota l'emperador Vespasià. A la seva mort va deixar a Plini part de les seves propietats.

Referències

Gens Minúcia
Qüestors
Pretors del segle I
Tribuns de la plebs del segle I
Jutges europeus


MINSK, 2 September (BelTA) – Belarus' Central Election Commission has accredited over 800 international observers for the parliamentary elections in Belarus on 11 September, reads a statement posted on the website of the Belarusian Central Election Commission, BelTA has learned.
According to the latest data, the CEC has accredited 330 observers from the CIS (including 44 from the CIS Inter-Parliamentary Assembly), 341 from the OSCE/ODIHR, 19 from PACE and 39 from the OSCE Parliamentary Assembly.
The CEC has also accredited 65 representatives of the diplomatic corps and 14 representatives of the electoral bodies of foreign states, including 3 from the Association of World Election Bodies (A-WEB).
Thus, the total number of foreign observers has increased to 811.
The elections to the House of Representatives of the Belarusian National Assembly are due on 11 September. The voters' list includes 6,990,696 citizens of Belarus.


At present the UK only accounts for around 2 percent of Russian imports, making it our twelfth biggest overseas market. Exports to Russia are running at around £2.4 billion a year. There is a demand for both Western goods and expertise. The most promising sectors are advanced engineering, financial services, ICT, power and energy, airports, construction, creative industries, rail and water. With Russia due to host the 2014 Winter Olympics there are also opportunities for sports and leisure infrastructure.
Russia also operates a number of Special Economic Zones offering benefits to businesses opting to set up in these locations. These zones often help Western businesses overcome problems accessing Russian markets.
Although a potentially lucrative market, many UK exporters may have qualms about doing business with Russia. There are many lingering myths, most of which are now unfounded.
However, it is essential for would-be exporters to undertake comprehensive strategic research of the opportunities looking at such things as the type of company to be set up, the delivery and distribution of products, effective marketing plans and, above all, local conditions.
UK businesses are likely to experience tough competition from European exporters such as Italy and Germany as well as those from Asia either because of their geographical proximity or long-standing trading relations.


text:
Earl of Dudley, of Dudley Castle in the County of Stafford (now the West Midlands), is a title that has been created twice in the Peerage of the United Kingdom, both times for members of the Ward family.

History
Dudley was first used for a peerage on 25 March 1341/42, when John Sutton became the first Lord Dudley of Dudley Castle. The male line failed at the 10th Baron, Sir Ferdinando Dudley, and Dudley Castle passed to his daughter, Frances Dudley, Baroness Dudley (1611–1697). She married Sir Humble Ward, the son of a wealthy goldsmith and jeweller to King Charles I (see Baron Dudley for more history of the Sutton family). Frances was given away in marriage by her grandfather Lord Dudley in order for him to be able to redeem the heavily mortgaged estates around Dudley, whose mineral resources were the foundation of the family's great wealth.

In 1644, Frances's husband Sir Humble Ward was raised to the Peerage of England in his own right as Baron Ward, of Birmingham in the County of Warwick. In contrast to the barony of Dudley, which had been created by writ, this peerage was created by letters patent and with remainder to heirs male. Lady Dudley and Lord Ward were both succeeded by their son Edward, the seventh and second Baron, respectively. He was styled Lord Dudley and Ward. He was succeeded by his grandson, the eighth and third Baron. He was the son of William Ward. On Lord Dudley and Ward's early death the titles passed to his posthumous son, the ninth and fourth Baron. He died unmarried at an early age and was succeeded by his uncle, the 10th and fifth Baron.

On his death in 1740, the two baronies separated. The barony of Dudley, which could pass through female lines, was inherited by the late Baron's nephew Ferdinando Dudley Lea (see the Baron Dudley for later history of this title). He was succeeded in the barony of Ward, which could only pass through male lines, by his second cousin John Ward, who became the sixth Baron Ward. He was the grandson of William Ward (d. 1714), second son of the first Baron. Lord Ward had earlier represented Newcastle-under-Lyme in the House of Commons. In 1763 he was created Viscount Dudley and Ward, of Dudley in the County of Worcester, in the Peerage of Great Britain. He was succeeded by his son from his first marriage, the second Viscount. He sat as Member of Parliament for Marlborough and for Worcestershire. He was childless and on his death the titles passed to his half-brother, the third Viscount. He was also Member of Parliament for Worcestershire. He was succeeded by his son, the fourth Viscount. He was a politician and served as Foreign Secretary from 1827 to 1828. In 1827 he was honoured when he was created Viscount Ednam, of Ednam in the County of Roxburgh, and Earl of Dudley, of Dudley Castle in the County of Stafford. Both titles were in the Peerage of the United Kingdom.

Lord Dudley was childless and on his death in 1833, the two viscountcies and earldom became extinct. He was succeeded in the barony of Ward by his second cousin Reverend William Humble Ward, the 10th Baron. He was the grandson of Reverend William Ward, younger brother of the first Viscount Dudley and Ward. He was succeeded by his eldest son, the 11th Baron.

In 1860, the viscountcy of Ednam and earldom of Dudley were revived when the 11th baron was created Viscount Ednam, of Ednam in the County of Roxburgh, and Earl of Dudley, of Dudley Castle in the County of Stafford. Both titles are in the Peerage of the United Kingdom. On his death the titles passed to his eldest son, the second Earl. He was a Conservative politician and served as Lord-Lieutenant of Ireland from 1902 to 1905 during the Irish Reform Association's plan for devolution in Ireland,  and as Governor-General of Australia from 1908 to 1911. He is commemorated by a Dudley Street in the Queen's Quarter of Belfast. He was succeeded by his eldest son, the third Earl of Dudley, who represented Hornsey and Wednesbury in the House of Commons as a Conservative. The Third Earl died in Paris on 26 December 1969.  the titles are held by his grandson, the fifth Earl, who succeeded his father in 2013.

Several other members of the Ward family have also gained distinction. William Dudley Ward, grandson of Humble Dudley Ward, second son of the 10th Baron Ward, was a Liberal politician. He married the socialite Freda May Birkin. Their daughter Penelope Dudley-Ward was a well-known actress. Sir John Hubert Ward (1870–1938), second son of the first Earl, was a major in the army and courtier. His son John Ward (1909–1990) was a colonel in the Life Guards. Robert Ward, third son of the first Earl, was Conservative Member of Parliament for Crewe. Edward Frederick Ward (1907–1987), third son of the second Earl, was a Group Captain in the Royal Air Force. George Ward, fourth and youngest son of the second Earl, was a Conservative politician and was created Viscount Ward of Witley in 1960. The actress Rachel Ward and her sister the environmental campaigner Tracy Louise Ward are both daughters of Peter Alistair Ward, third son of the third Earl.

The family seat of the Earls of Dudley was Himley Hall until the 1830s, after which Witley Court served as the main residence along with Dudley House. Witley Court was sold in 1920 and became derelict after a fire in 1937. The 1st Earl of Dudley of the 1860 creation was originally buried in the crypt of Saint Michael and All Angels Church in Great Witley, but was later moved to Worcester Cathedral where he is commemorated with a large funerary monument. His more recent successors – including the 4th Earl and his wife – rest in a private burial ground at Himley. Located at the rear of Himley's parish church, it is laid out as a memorial garden and normally closed to the public.

Barons Ward (1644) of Birmingham
Humble Ward, 1st Baron Ward (1614–1670)
Edward Ward, 7th Baron Dudley, 2nd Baron Ward (1631–1701)
Edward Ward, 8th Baron Dudley, 3rd Baron Ward (1683–1704)
Edward Ward, 9th Baron Dudley, 4th Baron Ward (1704–1731)
William Ward, 10th Baron Dudley, 5th Baron Ward (1685–1740)
John Ward, 6th Baron Ward (1700–1774) (created Viscount Dudley and Ward in 1763)

Viscounts Dudley and Ward (1763)
John Ward, 1st Viscount Dudley and Ward (1700–1774)
John Ward, 2nd Viscount Dudley and Ward (1725–1788)
William Ward, 3rd Viscount Dudley and Ward (1750–1823)
John William Ward, 4th Viscount Dudley and Ward (1781–1833) (created Earl of Dudley in 1827)

Earls of Dudley, First Creation (1827)
John William Ward, 1st Earl of Dudley (1781–1833)

Barons Ward (1644; Reverted)
William Humble Ward, 10th Baron Ward (1781–1835)
William Ward, 11th Baron Ward (1817–1885) (created Earl of Dudley in 1860)

Earls of Dudley, Second Creation (1860)
William Ward, 1st Earl of Dudley (1817–1885)
William Humble Ward, 2nd Earl of Dudley (1867–1932)
William Humble Eric Ward, 3rd Earl of Dudley (1894–1969)
William Humble Davis Ward, 4th Earl of Dudley (1920–2013)
William Humble David Jeremy Ward, 5th Earl of Dudley (b. 1947)

Present peer
William Humble David Jeremy Ward, 5th Earl of Dudley (born 1947), also known as David Dudley, is the son of the 4th Earl and his wife Stella Carcano y Morra. He was educated at Eton College and Christ Church, Oxford, and was styled as Viscount Ednam between 1969 and 2013.

On 3 July 1972 Dudley married firstly Sarah Mary Coats, daughter of Captain Sir Alastair Francis Stuart Coats, 4th Baronet, and his wife Lukyn Gordon; they were divorced in 1976, and in the same year he married secondly Debra Louise Pinney, daughter of George Robert Pinney. They were divorced in 1980, after having one child, Bethany Rowena Ward (born 1977).

In 2003, Dudley was living at Villa Montanet, Les Garrigues, Goult-Gordes, France. On 16 November 2013 he succeeded to the peerages.

The heir presumptive to the peerages is the present peer's younger half-brother Leander Grenville Dudley Ward (born 1971).

Line of succession
Leander Grenville Dudley Ward (b.1971) brother of the 5th Earl
Alexander Evelyn Giles Ward (b.1961) grandson of the 3rd Earl
Archibald Rupert William Ward (b.1993) son of Alexander Ward
Jeremy Christopher Ward (b.1975) grandson of the 3rd Earl
Hector Geordie Ward (b.2009) son of Jeremy Ward
Benjamin Robin Ward (b.1978) grandson of the 3rd Earl
Rupert Michael Ward (b.1947) grandson of the 2nd Earl
Eric Roderick Humble Ward (b.1973) son of Rupert Ward

See also

Baron Dudley
Viscount Ward of Witley
Dudley Castle

References

Further reading

Grazebrooke, H. S. 'The Barons of Dudley' Staffs. Hist. Coll. IX(2).
Kidd, Charles, Williamson, David (editors). Debrett's Peerage and Baronetage (1990 edition). New York: St Martin's Press, 1990,
Hemingway, John. An Illustrated Chronicle of the Castle and Barony of Dudley 1070-1757 (2006) The Friends of Dudley Castle.
Order for the Succession of the Earls of Dudley, Edward Ward, Frances Ward, John Levet Esq., Journal of the House of Lords, 1699, British History Online

Earldoms in the Peerage of the United Kingdom

Extinct earldoms in the Peerage of the United Kingdom
Noble titles created in 1827
Noble titles created for UK MPs
Noble titles created in 1860
Staffordshire
Earl
1644 establishments in England


text:
Seven myths about equity release
When it comes to equity release, there are a lot of myths.
The ability to borrow money for life, against the value of your property, is an option for some people in retirement.
You might need the money to top-up your pension income, cover the cost of home improvements, or make a financial gift to family members.
It's no surprise that equity release comes with a whole host of misconceptions and myths; it's a reasonably complicated financial product, after all!
In a new blog post, SunLife's equity release director Simon Stanney has tackled seven of the biggest myths surrounding equity release.
The first myth is that equity release is unregulated.
Equity release was unregulated in the past, but it's not anymore. These days, all equity release providers and financial advisers are regulated by the Financial Conduct Authority (FCA). There's another layer of consumer protection too, in the form of the Equity Release Council, a trade body representing the equity release sector.
The Equity Release Council ensures that all members follow their Statement of Principles, including a 'no negative equity' guarantee, which means you never pay back more than the value of your home.
Another principle they police is 'security of tenure', guaranteeing you can stay in your home for the rest of your life.
The second myth is that you can't use equity release because you still have a mortgage.
According to research by SunLife, one of the top five reasons why people use equity release is to pay off an existing mortgage.
Their research found that 65% of over 55s wrongly believed that having a mortgage means you can't use equity release.
If you have a mortgage and take out equity release, you need to release enough money to clear the existing mortgage or any other debt that is secured on your property. Once those debts are cleared, the balance of the equity release can be spent as you please.
The third equity release myth is that you can't leave behind an inheritance.
The research found that a quarter of over 55s thought taking out equity release meant they could not leave behind an inheritance.
While using equity release means you cannot leave behind the value of your house for your loved ones, they can still inherit any remaining monies after the equity release loan is paid off.
If you want to use equity release and guarantee an inheritance for your family, you can ringfence some of the value of your home to leave behind.
Equity release myth number four is that using equity release will leave your family in debt.
FCA regulation and the Equity Release Council principles mean that any equity release plan carries the 'no negative equity' guarantee, so you cannot leave your family with your debt.
Even though the amount of equity released, plus interest added, will be a debt against your home, the amount charged by the equity release provider will never exceed the value of the property. This means the equity release debt will always be covered by the sale of your home, either when you die or should you move into a residential care home.
The fifth myth is that you could lose your home or be forced to move out.
Once again, this is where the Equity Release Council principles come into play, with the 'security of tenure' guarantee.
When you use a lifetime mortgage, you remain the legal owner of your home.
With home reversion plans, you sell part or all of your home in exchange for a cash lump sum, but continue to live there, rent-free, until the house is sold, you die, or move into residential care.
Myth number six about equity release is that you can never move home again.
More than half of homeowners over 55 believe that if they take equity from their home, they will be stuck in that property forever.
However, assuming you meet the criteria of the equity release provider, you can move home and take the equity release plan with you.
There will, of course, be some costs associated with moving home with the plan. But all costs will be fully explained before you take out the equity release plan.
Myth number seven, the final equity release myth, is that the cash from equity release is taxable.
SunLife's research found that 55% of over 55s didn't realise that the cash from equity release is tax-free. There's no income tax or capital gains tax to pay on the money released under equity release.
You should note that the amount of cash you have in savings can have an impact on your state benefits, so always take care to check your benefits eligibility first.
Equity release can offer a solution for many over 55 homeowners looking for a boost to their finances, but it is not for everyone. Getting advice is a necessity and it is also important to talk things over with family and loved ones because taking out equity release is likely to affect them too by reducing their inheritance.
If you are considering equity release and would like to discuss your situation and options, contact Kellands today.
You have to get advice before releasing tax-free cash from your home.


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Sarah Storey: frightening course ruined my National 10
sarah storey, storey, national 10, ten, tt, ten champs, ctt, rttc
Sarah Storey has vented frustration with the organisers of the National 10 on Saturday, saying that traffic on the time trial course made it dangerous for riders and ruined her ride.
"I really hated every second I was on the road," she told Cycling Weekly. "I have never been so frightened on the road. I had an absolute horror and I couldn't wait to get off the road."
"I've never experienced anything like that many cars during a time trial before," she continued. "There were no warnings for motorists. Cars were coming past so close. I was worried about the Juniors, who went out at 2 o'clock – at the peak of the traffic. It was dangerous."
The time trial course took the riders down a national speed limit A-road to a junction and back again.
Cycling Weekly's reporter at the event noted that the strong winds will have made it hard for riders to be able to hear cars behind them, and a number of riders expressed alarm at the passing cars after the event.
Storey finished fourth, and feels that the dangerous nature of the road adversely affected her performance.
"My average power was quite a lot down," she said. "It came from not being able to concentrate properly on my ride. I was riding to get through it. My power output average was down by 15-20w."
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