text:
\section{\label{sec1}Introduction}

Richard Feynman in his lecture "the character of physical law"~\citep{Feynman1965} has outlined a series of crucial unsolved problems of modern physics.
Among them there is an unfilled gap between quantum mechanics and the physics of large scale motion in the universe. Predominantly, it is a theory of quantum gravitation
The lecture encourages physicists to search for these solutions~\citep{Hajdukovic2013}.

Relativistic hydrodynamics~\citep{Font2008, LaigleEtAl2014, WilsonMathews2003} perhaps can cover this wide  region
of the scientific interest.
 Its scope of interests spreads from physics of plasma up to neutron stars, black holes, supernovae, compact binary systems, dense clusters, collapsing stars, the early universe, etc~\citep{WilsonMathews2003}.

Here we shall consider the relativistic hydrodynamical equations in the light of a description of the superfluid vacuum medium - the medium consisting of  enormous amount of virtual pairs of particles-antiparticles with opposite orientations of spins. That is, the pairs possess zero spin~\citep{Volovik2003}.

We shall try to trace the emergence of the quantum equations (the Klein-Gordon equation and in the non-relativistic limit the Schr\"odinger equation) from the relativistic hydrodynamical equation + the continuity equation. It turns out, that for solving this task, we need to find the quantum potential through applying the internal pressure to Fick's laws.

Second, we shall try applying the relativistic hydrodynamical equation for the description of the motion of spiral galaxies. Here we introduce a viscosity of the medium which is equal to zero in averaged on time but has a non-zero dispersion~\citep{Sbitnev2015b, Sbitnev2015c}. Due to this trick we find that the orbital velocity of the spiral galaxy attains flat level at large distances from the galactic center. Essentially, fluctuations of the viscosity about zero describes exchanging energy of the orbital rotation with the zero-point fluctuations of the physical vacuum on the ultra-low frequencies.
Figuratively speaking, the dark matter appears to us as the ultra-low vacuum fluctuations.

Here we first outline the general formulas which will then be used further.

The relativistic hydrodynamics starts from a description of the energy-momentum tensor~\citep{RezzollaZanotti2013}
\begin{equation}
  T^{\,\mu\nu} = (\epsilon + p){\mathit u}^{\mu}{\mathit u}^{\nu} + \,p \eta^{\,\mu\nu}.
\label{eq=1}
\end{equation}
 Here $\epsilon$ and $p$ are the functions per unit volume.
They are expressed in units of pressure, Joule/m$^3$~=~Pa.
The metric tensor $\eta^{\,\mu\nu}$ has the spacelike signature $(- + + +)$.
  The 4-velocity ${\mathit u}^{\mu}=\gamma(1,{\vec{\mathit v}})$ meets the condition
  ${\mathit u}_{\mu}{\mathit u}^{\mu}=-1$ where $\gamma = (1-{\mathit v}^2)^{-1/2}$~\citep{Romatschke2010a}.
 Here we follow the convention that the units of space and time are chosen such that $c=1$. However, sometimes we shall use the International System of Units where the speed of light has the customary value equal about $3\cdot10^{8}$ m/s.

The four-gradient (both covariant and contravariant) and the four-laplacian (the d'Alembert operator)
 compactly written read:
\begin{eqnarray}
\nonumber
&&\hspace{-8pt}
  \partial_{\mu} = \biggl( {{}{}} {{\partial\;}\over{\partial\,\tau}}, \nabla\biggr), ~
  \partial^{\,\mu} = \eta^{\,\mu\nu}\partial_{\nu} =  \biggl(- {{}{}} {{\partial\;}\over{\partial\,\tau}}, \nabla\biggr), \\
&&\hspace{-8pt}
 \partial_{\mu}\partial^{\,\mu} = \partial_{\mu}\eta^{\,\mu\nu}\partial_{\nu} =
 -{{}{}} {{\partial^2\;}\over{\partial\,\tau^2}} + \nabla^2.
\label{eq=2}
\end{eqnarray}
 Since  we adopted $c=1$  length is measured here in  unit of $\tau=tc$.
We shall write either $\partial\tau$ or $c\,\partial\,t$
when the customary units of time are needed.
In the last case we write ${\widetilde\partial}_{\mu}$ and~${\widetilde\partial}^{\mu}$.

An initial step in studying the relativistic hydrodynamical flows begins from writting the conservation laws of  energy and momentum $\partial_{\mu}T^{\,\mu\nu}=0$~\citep{WilsonMathews2003, LandauLifshitz1987}. Here we need to be careful. Our task is to write the relativistic equations of hydrodynamics, which would took into consideration quantum effects.  Appearance of the quantum potential in the course of computations gives guaranty that the computations are correct~\citep{Sbitnev2015b, Sbitnev2015c}.
This potential is a fundamental element, which creates a geometrodynamic picture of the quantum world in the non-relativistic domain, a relativistic curved space-time background, and the quantum gravity domain~\citep{Fiscaletti2012}.

 A final aim of the computations is to derive the  Klein-Gordon equation and the Schr\"odinger equation in the non-relativistic limit.
With this aim in  mind, we rewrite the conservation law in the following view
\begin{equation}
\partial_{\mu}(T^{\mu\nu}/\rho)=0.
\label{eq=3}
\end{equation}
Observe that the terms ${{(\epsilon+p)}/{\!\rho}}$ and  $p/\!\rho$ have dimensions of energy.
Here $\rho$ is the density distribution of the virtual particles populating the medium.
It is equal to number of the sub-particles per unit volume, $\rho = n/\Delta V$~\citep{JackiwEtAl2004}.

The article is organized by the following manner.
Sec.~\ref{sect2} deals with the perfect fluid. It  consists of two subsections.
 In the first subsection we define relativistic  Fick's laws,
 and from here we compute the relativistic quantum potential.
The second subsection considers the scalar field $S + \hbar\omega\gamma^{-1}t$
based on which the Klein-Gordon equation in the relativistic limit
and the Schr\"odinger equation in the non-relativistic limit are derived.
Sec.~\ref{sect3} considers a relativistic non-perfect fluid, that is the viscous fluid.
We get the relativistic Navier-Stokes equation and further we get the equation for the vorticity.
The vorticity and the orbital speed are considered for the case of the electron-positron pair.
Sec.~\ref{sect4} considers formation of the vortex on the galactic scales.
Formation of the flat orbital speed for the rotating spiral galaxy is the subject of consideration.
Sec.~\ref{sec5}  summarizes the results.

\section{\label{sect2}Relativistic perfect fluid:
 derivation of the Klein-Gordon and Schr\"odinger equations}

It turns out, that the equation~(\ref{eq=3}) can be reduced
 either to the Klein-Gordon equation or to the Schr\"odinger equation
 depending on the relativistic or non-relativistic limit.
However we first should show that the term ${\mathit p}/\rho$ is nothing like the quantum potential.
With this aim in  mind, we need to use  the relativistic Fick's laws.
Here we shall write the partial derivatives~(\ref{eq=2})
writing down $c\,\partial\,t$  rather than  $\partial\tau$.
Let us begin.

\subsection{\label{subsect2A}The Fick's law in the relativistic sector}

The first Fick's law in the relativistic limit has the following form
\begin{equation}
 {\mathit j}_{\mu} = - D{ {\widetilde\partial}_{\mu}}\rho_{_{M}}
\label{eq=4}
\end{equation}
 Here $D$ is the diffusion constant having the dimension of length$^2$/time.
 The law~(\ref{eq=4}) says that diffusion flux vector, ${\mathit j}_{\mu} = ({\mathit j}_{0}, {\vec{\mathit j}})$, is induced by the inhomogeneous distribution of the mass density $\rho_{_{M}}$ within the 4D space-time volume.
 Here
$\rho_{_{M}}=M/{\delta V} = mn/{\Delta V}=m\rho$~\citep{JackiwEtAl2004, Sbitnev2015c}
and the mass $M=mn$ is that of the volume $\Delta V$ of the medium in question
($m$ is the mass of the single sub-particle
and $n$ is the amount of them populating the volume ${\Delta V}$~\citep{JackiwEtAl2004}).

Not to be confused the diffusion flux vector ${\mathit j}_{\mu}$ with the density current
${\mathit J}_{\mu} = \rho_{_{M}}{\mathit u}_{\mu}$~\citep{Font2008, RezzollaZanotti2013},
 where ${\mathit u}_{\mu}$  is the fluid 4-velocity and $\rho_{_{M}}$ is the proper rest-mass density.
 The diffusion flux vector ${\mathit j}_{\mu}$ can be seen as a result of scattering of the sub-particles
 on each other due to the collisions.

We need to define the diffusion coefficient~$D$.
First we introduce a hypothesis that all space-time is filled with virtual radiations with  frequency $\omega$.
So, we define
\begin{equation}
  D = {{1}\over{\epsilon_{0}\mu_{0}\,\omega}} = {{c^{2}}\over{\,\omega}}.
\label{eq=5}
\end{equation}
Here $c=1/\sqrt{\epsilon_{0}\mu_{0}}$ is the light speed in the physical vacuum,
and $\epsilon_{0}$, $\mu_{0}$ are the absolute dielectric permittivity of classical vacuum and
the vacuum permeability, respectively.
 Observe that the zero-point energy of the radiation is $E =\hbar\omega/2$.
The radiation is due to motions of the virtual particles with the proper mass $m$.
So we may write $E = mc^2$
 and consequently
\begin{equation}
  D = {{\hbar}\over{2m}}
\label{eq=6}
\end{equation}
 Here $\hbar$ is Planck's reduced constant.

In the light of this vision we may imagine that motions of the virtual particles have a weak dispersion around a certain  average. We may guess that the virtual particles on this level undergo collisions with each other like the Brownian particles.
Here we draw on the hypothesis put forward by Edward Nelson
about aether populated by the Brownian sub-particles~\citep{Nelson1966}.
However, in contrast to the quasi-classical collisions of the Brownian sub-particles in our case the diffusion is achieved due to the uncertaintly principle
- the collisions induce uncertainty of momenta of the scattered sub-particles~\citep{Sbitnev2013a}.

 Next we proclaim that the pressure $p$ consists of sum of two pressures, $p_{1}$ and $p_{2}$. And the pressure $p_{1}$ follows from the Fick's laws.
The first Fick's law says that the diffusion flux, ${\mathit j}_{\mu}$, is proportional to the negative value of the density mass gradient~(\ref{eq=4}).
One can see
 that the four-laplacian $D {\widetilde\partial}^{\,\mu}{\mathit j}_{\mu}
= -D^2\, {\widetilde\partial}^{\,\mu} {\widetilde\partial}_{\mu}\rho_{_{M}}$
has the dimension of the pressure. So, we write
\begin{equation}
p_{1} = -D^{2}
\biggl(
  \nabla^2 \rho_{_{M}}    -    {{1}\over{c^2}}{{\partial^2\;}\over{\partial t^2}}\rho_{_{M}}
\!\biggr).
\label{eq=7}
\end{equation}
As for the pressure  $p_{2}$, one can note first that the kinetic energy of the diffusion flux is
$(m/2)({\mathit j}^{\,\mu}{\mathit j}_{\mu}/\rho_{_{M}}^{2})$.
It means that there exists one more pressure as the kinetic energy  per unit volume of the medium in question:
\begin{equation}
 p_{2} =  {{D^2}\over{2\rho_{_{M}}}}
  \biggl(\!
     (\nabla \rho_{_{M}})^{2}
 -        \biggl(
               {{1}\over{c}}{{\partial}\over{\partial t}}\rho_{_{M}}
          \biggr)^{\!2\,}
   \biggr).
\label{eq=8}
\end{equation}

 Now we can see that sum of the two pressures, $p_1 + p_2$, divided by $\rho$ (we remark that $\rho_{_{M}} = m\rho$)  reduces to the quantum potential
\begin{eqnarray}
\nonumber
   Q &=& {{p_{1}+p_{2}}\over{\rho}} =
-{{\,\hbar^{2}}\over{4m\rho}}
\biggl(
        \nabla^2 \rho    -   { {{1}\over{c^2}} {{\partial^2\;}\over{\partial t^2}}}\rho
\biggl)
\\ \nonumber
&&\hspace{54pt}
+{{\,\hbar^{2}}\over{8m \rho^2}}
\biggr(\!
   \bigr(
          \nabla \rho
    \bigl)^{\!2}
-   \biggl(
           {{1}\over{c}} {{\partial}\over{\partial t}}\rho
    \biggr)^{\!2}
\biggr)
\\
=&-&{{\,\hbar^2}\over{2mR}}
\biggl(
   \nabla^2 - {{1}\over{c^2}} {{\partial^2\;}\over{\partial t^2}}
\biggr) R
 = - {{\hbar^2}\over{2m}}{{{\partial}_{\mu}{\partial}^{\,\mu}R}\over{R}}.
 \hspace{24pt}
\label{eq=9}
\end{eqnarray}
 Here $R = \sqrt{\rho}$.
  When ${\mathit v}=1$ the quantum potential
 is in complete concordance with that given in~\citep{Nikolic2007}.
On the other hand, when ${\mathit v}\rightarrow0$
this potential degenerates to the non-relativistic one.

\subsection{\label{subsect2B}Scalar field in a general case}

 Return to Eq.~(\ref{eq=3}).
Since the tensor $T^{\mu\nu}$ is symmetric, one can believe that it comes from the scalar field.
After multiplying this equation by $\eta^{\mu\nu}\eta_{\nu\mu}=1$
 and taking into account that
${\partial}_{\mu}\eta^{\mu\nu}\eta_{\nu\mu}{\mathit u}^{\mu}{\mathit u}^{\nu}
={\partial}^{\,\nu}{\mathit u}_{\,\nu}{\mathit u}^{\nu}$
 we have
\begin{equation}
\hspace{-8pt}
  \biggl(\!{{\epsilon + p}\over{\rho}}\gamma\!\biggr) {\partial}^{\,\nu}{\mathit u}_{\,\nu}{\mathit u}^{\,\nu}
 \!-\! {\partial}^{\,\nu} \biggl(\!{{\epsilon + p}\over{\rho}}\gamma\!\biggr)
 + {\partial}^{\,\nu} Q = 0.
\label{eq=10}
\end{equation}
In front of the second member we write minus
 inasmuch as ${\mathit u}_{\,\nu}{\mathit u}^{\nu}=-1$.

Keeping in mind the Klein-Gordon equation in perspective
we first multiply Eq.~(\ref{eq=10}) by 2 and suppose that
\begin{equation}
  mc^2 = 2{{(\epsilon + p)}\over{\rho}}\gamma.
\label{eq=11}
\end{equation}
The mass $m$ hereinafter is $m_{0}\gamma$, where $m_{0}$ is the rest mass and $\gamma = (1-v^2)^{-1/2}$.
Also  we write the letter $c$ meaning the speed of light, which is adopted as 1 according to our convention.
Inasmuch as the superfluid medium is irrotational, the first term of Eq.~(\ref{eq=10})
 is rewritten as ${\partial}^{\,\nu}{\mathit u}_{\,\nu}{\mathit u}^{\,\nu}
= {\mathit u}^{\,\nu}{\partial}^{\,\nu}{\mathit u}_{\,\nu}
+ \eta^{\nu\mu}{\mathit u}_{\,\mu}{\partial}^{\,\nu}\eta_{\nu\mu}{\mathit u}^{\,\mu}
={\partial}^{\,\nu}{\mathit u}^{2}$.
The solution of Eq.~(\ref{eq=10}) is as follows
\begin{equation}
   m{\mathit v}^{2} - mc^2 +2Q = 2C.
\label{eq=12}
\end{equation}
 Here ${\mathit v}_{\mu}={\mathit u}_{\mu}c$ and $C$ is the integration constant
having dimension of energy.
Since the superfluid medium under consideration is irrotational, we can express the velocity ${\mathit v}_{\mu}$ through the gradient of the scalar field $S+\hbar\omega\gamma^{-1}t$.
The last extra term vanishes as $\gamma^{-1}$ tends to zero (the relativistic sector),
but this term will be important in the non-relativistic limit when getting the Schr\"odinger equation.
So, the velocity ${\mathit v}_{\mu}$ can be expressed as follows
\begin{eqnarray}
\nonumber
&&  {\mathit v}_{\mu} = -{{1}\over{m}} {\partial}_{\mu}(S+E{\gamma}^{-1}t)
= -{{1}\over{m}} {\partial}_{\mu}S - {{E}\over{mc\gamma}}, \\
\nonumber
&&
  {\mathit v}^{2} = {{1}\over{m^2}}{\partial}_{\mu}\,(S+E{\gamma}^{-1}t){\partial}^{\,\mu}(S+E{\gamma}^{-1}t) \\
&=&
  {{1}\over{m^2}}{\partial}_{\mu}\,S{\partial}^{\,\mu}S
+  {{2E}\over{\gamma m^2c}}{\partial}_{\,0}\,S
+  {{E^2}\over{\gamma^{2}m^2c^2}}.
\label{eq=13}
\end{eqnarray}
 Here we need to say some words about the phase $\omega\gamma^{-1}t$.
 It comes from the expression ${\Delta t} = {\Delta t_{_{0}}}\gamma$ describing the time dilation.
This phase belonging to the unitary group $U(1)$ carries out the timekeeping of  the path $tc$~\citep{Poluyan2005}.
 It is seen that the timekeeping tends to zero as $\gamma^{-1}$ tends to zero, that is, as  ${\mathit v}\rightarrow 1$.
The energy of the timekeeping is defined as $E = \hbar\omega = m_{0}c^2$. Where $m_{0}$ is the rest mass. Its contribution disappears  as the velocity approaches the speed of light.

Now multiplying  Eq.~(\ref{eq=12}) by $m$  we  rewrite it in details
\begin{eqnarray}
\nonumber
&&
\underbrace{ \partial_{\mu} S \partial^{\,\mu} S}_{\rm (a)}  +
\underbrace{ {{2E}\over{c\gamma}}\partial_{\,0} S + {{E^2}\over{c^2{\gamma}^2}} }_{\rm (b)}
\\
&&
   -   m^2c^2   -  {\hbar^2}\, {{\partial_{\mu} \partial^{\,\mu} R }\over{R}} = 2mC.
\label{eq=14}
\end{eqnarray}
Let us add to this equation for pair also the continuity equation~\citep{Fiscaletti2012}
\begin{equation}
  \partial_{\,\mu} ( \rho\,\partial^{\,\mu}S ) = 0.
\label{eq=15}
\end{equation}

The parameter $\gamma = (1-{\mathit v}^{2})^{-1/2}$ presented in the denominators of the two terms
 enclosed in the brace (b) in Eq.~(\ref{eq=14}) determines transition to either the relativistic limit or
to the non-relativistic limit.

\subsubsection{\label{subsubsect2B1}Relativistic sector}

 At relativistic limit, ${\mathit v}\rightarrow 1$, $\gamma$ tends to infinity.
 In this case the terms enclosed in the brace (b) in Eq,~(\ref{eq=14}) vanish and we have
\begin{equation}
 \partial_{\mu} S \partial^{\,\mu} S    -   m^2c^2   -  {\hbar^2}\, {{\partial_{\mu} \partial^{\,\mu} R }\over{R}}
 = 2mC.
\label{eq=16}
\end{equation}
 The both equations, Eqs.~(\ref{eq=15}) and~(\ref{eq=16}),
are extracted from the Klein-Gordon equation
\begin{equation}
 \partial_{\mu}\partial^{\,\mu} \psi +
 {{m^2c^2}\over{\hbar^2}}\psi + {{2m}\over{\hbar^2}}C\psi = 0
\label{eq=17}
\end{equation}
 as soon as we substitute in this equation the wave function $\psi$ represented in the polar form
\begin{equation}
  \psi = R \exp\{ {\bf i}S/\hbar \}
\label{eq=18}
\end{equation}
 and separate the solutions into the real, Eq.~(\ref{eq=16}), and imaginary, Eq.~(\ref{eq=15}), parts.
 Here $R=\rho^{1/2}$ is the amplitude of the wave function and $S/\hbar$ is its phase.
The probability density $\rho({\vec r},t) = R(\vec r,t)^2$ shows distribution of the virtual particles in the vicinity of the 4-point $(t,{\vec r})$. Whereas the action $S({\vec r},t)$ characterizes a degree of mobility of these particles in the same place.

 Computations done above give a good concurrence with those
 that have been fulfilled by Fiscaletti~\citep{Fiscaletti2012}. In his work the quantum Hamilton-Jacobi
equation has a view
\begin{equation}
   \partial_{\mu} S \partial^{\,\mu} S = m^2c^2 (1 + {\widetilde Q})
\label{eq=19}
\end{equation}
with the quantum potential defined as
\begin{equation}
 {\widetilde Q} = {{\hbar^2}\over{m^2c^2}}{{1}\over{R}}
 \biggl(
   \nabla^{2} - {{1}\over{c^2}}{{\partial^2\,}\over{\partial\,t^2}}
 \biggr) R.
\label{eq=20}
\end{equation}\\
Comparing Eqs.~(\ref{eq=16}) and~(\ref{eq=19})  we find their good concurrence when $C = 0$.
The difference in the quantum potentials~(\ref{eq=9}) and~(\ref{eq=20})
 is due to their  individual  definitions.
The potential $Q$ has the dimension of energy, whereas ${\widetilde Q}$ is dimensionless due to dividing by $mc^2$.
Opposite signs at the quantum potentials
 are due the choice of the metric tensors, $\eta_{\mu\nu}$ or $g_{\mu\nu}$, having the opposite signatures
 $(- + + +)$ and $(+ - - -)$, respectively.

\subsubsection{\label{subsubsect2B2}Non-relativistic sector}

At non-relativistic limit ${\mathit v}\rightarrow 0$. It means that $\gamma$ converges to unit.
 Observe that in this limit the third and fourth terms in Eq.~(\ref{eq=14}) kill each other, $E^2/c^2 - m_{0}^2c^2 = 0$.
First we rewrite the term enclosed in the brace (a) in Eq.~(\ref{eq=14}) in the form
${\partial_{\mu}}S{\partial^{\mu}}S = {\partial_{\,0}}S{\partial^{\,0}}S +(\nabla S)^2$, where
$\partial_{\,0} = \partial/\partial\tau$ and $\tau = ct$.
So, we need to compare $\partial S/\partial t$ and $E = m_{0}c^2$.
In the non-relativistic limit we have the following inequality $m_{0}c^2 \gg \partial S/\partial t$.
So we can rewrite Eq.~(\ref{eq=14}) as follows
\begin{equation}
{{\partial }\over{\partial\,t}}S + {{1}\over{2m_{0}}}(\nabla S)^2
-{{\hbar^2}\over{2m_{0}}}{{\nabla^{\,2}R}\over{R}} = C.
\label{eq=21}
\end{equation}

 This equation is the modified Hamilton-Jacobi equation because of the quantum potential loaded to it.
 This equation is supplemented by the continuity equation~\citep{Fiscaletti2012}:
\begin{equation}
 {{\partial\,\rho}\over{\partial\,t}}
 + \nabla \biggl(
                          \rho\,{{\nabla S}\over{m_{0}}}
                \biggr) = 0.
\label{eq=22}
\end{equation}
  Here the density distribution $\rho = R^2$
 and $\nabla S/m_{0} = {\vec{\mathit v}}$ is the current velocity.
 These equations, Eqs.~(\ref{eq=21}) and~(\ref{eq=22}), are extracted from
 the following Schr\"odinger equation
\begin{equation}
  {\bf i}\hbar {{\partial\,\psi}\over{\partial\,t}} =
- {{\hbar^{2}}\over{2m_{0}}}\nabla^{2} \psi  -C \psi.
\label{eq=23}
\end{equation}
 By substituting into this equation the wave function $\psi$ represented in the polar form~(\ref{eq=18})
and separating on real and imaginary parts we come to Eqs.~(\ref{eq=21}) and~(\ref{eq=22}), respectively.

\section{\label{sect3}Relativistic non-perfect fluid:
   vortex tubes and others}

In previous chapter we considered the perfect relativistic fluid. It represents, in fact, the superfluid medium. By adopting it as the physical vacuum we have derived the quantum equations in assumption of existence of the scalar field $S$ gradient of which gives the fluid velocity. Next let us add to
the energy-momentum tensor~(\ref{eq=1})
 a term describing the viscosity of the fluid~\citep{RezzollaZanotti2013}
\begin{equation}
\hspace{-16pt}
 T^{\,\mu\nu} =  (\epsilon + p){\mathit u}^{\mu}{\mathit u}^{\nu} + p \eta^{\,\mu\nu}  + {\Pi}^{\mu\nu}
\label{eq=24}
\end{equation}
 A new  term ${\Pi}^{\mu\nu}$ embedded in this equation is the viscous stress tensor~\citep{Romatschke2010a}.
In the general case we represent it in the following view~\citep{RezzollaZanotti2013}
\begin{equation}
 \Pi^{\mu\nu} =
\mu c(\partial^{\mu}{\mathit u}^{\nu} + \partial^{\nu}{\mathit u}^{\mu})
  + c\biggl(
             \zeta - {{2}\over{3}}\mu
     \biggr)
     \partial^{\,\mu}{\mathit u}_{\mu}\eta^{\,\mu\nu}.
\label{eq=25}
\end{equation}
Since the dimensionality of the viscosity coefficients, shear $\mu$ and bulk $\zeta$, is Pa$\cdot$s and the dimension of $c\,\partial^{\mu}{\mathit u}^{\nu}$ is s$^{-1}$, the dimension of $\Pi^{\mu\nu}$ is Pa = Joule/m$^3$.

We shall consider the incompressible fluid. It means that $\nabla\rho=0$.
The conservation law of the energy-momentum tensor takes the form
\begin{eqnarray}
\nonumber
\hspace{-18pt}
   \partial_{\mu} \biggl({{T^{\mu\nu}}\over{\!\rho}}\biggr)
& =&
 \partial_{\mu}  \biggr(\!{{\epsilon+p}\over{\!\rho}}\gamma {\mathit u}^{\mu}{\mathit u}^{\nu} \!\biggl)
 \\
\hspace{-18pt}
&+& \partial^{\,\nu} Q
\;+\; \partial_{\mu} (\mu(t)/\rho)  \pi^{\mu\nu}     = 0.
\label{eq=26}
\end{eqnarray}
 Here $Q=p/\rho$ is the quantum potential, due to which transition to the quantum equations can be assured.
The term $\pi^{\mu\nu}$ has a view
\begin{equation}
  \pi^{\mu\nu} =
c (\partial^{\mu}{\mathit u}^{\nu} + \partial^{\nu}{\mathit u}^{\mu})
              - c{{2}\over{3}}
     \partial^{\,\mu}{\mathit u}_{\mu}\eta^{\,\mu\nu}.
\label{eq=27}
\end{equation}
 For the sake of simplicity, we take further into account only the shear viscosity.
Note that the viscosity we believe is a function of time~\citep{Sbitnev2015b, Sbitnev2015c}.
 We suppose that the viscosity average on time vanishes.
 But its variance is non-zero.
 It means that the parameter $\mu(t)$ is a fluctuating quantity about zero.
 This supposition is a very impressive.
We hope to obtain long-lived vortices having non-zero vorticity's  cores~\citep{Sbitnev2015b, Sbitnev2015c}.
But first let us show that the equation $\partial_{\mu}(T^{\mu\nu}/\rho)=0$ can be reduced to the relativistic
Navier-Stokes equation. Here we repeat the computations of J.~W.~van~Holten~\citep{Holten2006}.

\subsection{\label{subsect3A}Relativistic form of the Navier-Stokes equation}

Let us split Eq.~(\ref{eq=26})  into the time and space components.
 The equation with $\nu=0$ becomes:
\begin{eqnarray}
\nonumber
&&  {{\partial}\over{\partial\tau}}\biggl(\!{{\epsilon+p}\over{\rho}}\gamma\!\biggr)
  + \nabla\!\cdot\!\biggl(\!
                            {{ \epsilon + p } \over {\rho }}\gamma  {\vec{\mathit v}}
                           \!\biggr) \\
 &+&  {{\partial\,Q}\over{\partial\tau}}
 +{{\partial (\mu(t)/\rho)}\over{\partial\tau}}  \cdot \pi^{0,0}
 + {{\mu(t)}\over{\rho}} \partial_{\mu}\pi^{\mu, 0}
  = 0,
\hspace{22pt}
\label{eq=28}
\end{eqnarray}
 whilst the space components with $\nu=i$ becomes
\begin{eqnarray}
\nonumber
 &&
{{\partial\;}\over{\partial \tau}}
            \biggl(
                    {{\epsilon+p}\over{\rho}}\gamma {\mathit v}_{i}
             \biggr)
 + \nabla_{}\!\cdot\!
             \biggl(
                     {{\epsilon+p}\over{\rho }}\gamma {\vec{\mathit v}}\!\cdot\!{\mathit v}_{i}
             \biggr)
\\
&+&\nabla_{i} Q +
 {{\partial(\mu(t)/\rho)}\over{\partial\tau}}  \cdot \pi^{0,i}
 + {{\mu(t)}\over{\rho}} \partial_{\mu}\pi^{\mu,i}
 = 0.
\hspace{22pt}
\label{eq=29}
\end{eqnarray}
 Here $\tau = ct$ and $i$ runs $1, 2, 3$.
 By replacing the derivatives of $(\epsilon+p)\gamma/\rho$ and $(\epsilon+p)\gamma {\vec{\mathit v}}/\rho$
 with the time and the direction  with relevant terms taken from Eq.~(\ref{eq=28})
 we obtain the following expression:
\begin{eqnarray}
\nonumber
&&
 {{\epsilon+p}\over{\rho}}\gamma
\biggl(\!
  {{\partial {\vec{\mathit v}}}\over{\partial \,\tau}} + ({\vec{\mathit v}}\!\cdot\!\nabla{\vec{\mathit v}})
\biggr)
+  \nabla_{}Q
 -  {\vec{\mathit v}} {{\partial\;}\over{\partial \,\tau}} Q
\\ \nonumber
 &&+ {{\partial(\mu(t)/\rho)}\over{\partial\tau}}
 \cdot (\pi^{0,i}  -  {\vec{\mathit v}}\, \pi^{0,0}) \\
&&
 + {{\mu(t)}\over{\rho}} (\partial_{\mu}\pi^{\mu,i}  -  {\vec{\mathit v}}\, \partial_{\mu}\pi^{\mu, 0})  = 0.
\label{eq=30}
\end{eqnarray}
 Recall that $\gamma = (1-{\mathit v}^2)^{-1/2}$.
 When ${\mathit v}$ tends to 1 the parameter $\gamma$ goes to infinity.
And this equation describes the fluid motion with relativistic velocities.
 Here we define
\begin{equation}
  m c^2 =  {{\epsilon+p}\over{\rho}}\gamma,
\label{eq=31}
\end{equation}
 where the relativistic mass $m$ is $m_{0}\gamma$, and $m_{0}$ is the rest mass.

 When ${\mathit v}$ tends to 0 the parameter $\gamma$ goes to 1, however.
It is the non-relativistic limit. Let us look into this limit.

\subsubsection{\label{subsect3A1}Non-relativistic limit}

 At non-relativistic limit, ${\mathit v}\rightarrow 0$, $\gamma$ converges to unit.
In this case $mc^{2}$ reduces to $m_{0}c^2$, where  $m_{0}$ is the rest mass.
Let the multiplier $c^2$ be shifted inside brackets in the first line of Eq.~(\ref{eq=30})
\begin{equation}
 m_{0} c^2
\biggl(\!
  {{\partial {\vec{\mathit v}}}\over{\partial \,\tau}} + ({\vec{\mathit v}}\!\cdot\!\nabla{\vec{\mathit v}})
\!\biggr)
=
 m_{0}
\biggl(\!
  {{\partial c{\vec{\mathit v}}}\over{\partial \,t}} + (c{\vec{\mathit v}}\cdot\!\nabla{c\vec{\mathit v}})
\!\biggr)
\label{eq=32}
\end{equation}
and call the term $c{\vec{\mathit v}}$ as the real velocity, ${\vec{\mathit V}}$, of the non-relativistic fluid.
Taking into account that the third and four terms in Eq.~(\ref{eq=30}) vanish in the non-relativistic limit
we come to the non-relativistic form of the Navier-Stokes equation
\begin{equation}
  m_{0}
\biggl(\!
  {{\partial {\vec{\mathit V}}}\over{\partial \,t}} + ({\vec{\mathit V}}\cdot\!\nabla{\vec{\mathit V}})
\!\biggr)
= \nabla Q
+ {{\mu(t)}\over{\rho}}\nabla^{2}  {\vec{\mathit V}}.
\label{eq=33}
\end{equation}
 For the sake of simplicity we cut the viscosity term up to
$(\mu(t)/\rho)\partial_{\,i}\partial^{\,i} c{\mathit v}^{i} \Rightarrow (\mu(t)/\rho)\nabla {\vec{\mathit V}}$,
as it is done for ease of analytical studies~\citep{Sbitnev2015b, Sbitnev2015c}.

Observe that the term $ ({\vec{\mathit V}}\cdot\!\nabla{\vec{\mathit V}})$
can be rewrite as follows
\begin{equation}
 ({\vec{\mathit V}}\cdot\!\nabla{\vec{\mathit V}})
 = \nabla {\mathit V}^2/2
 + [{\vec\omega}\times{\vec{\mathit V}}].
\label{eq=34}
\end{equation}
 The first term multiplied by the  mass $m_{0}$ is gradient of the  kinetic energy.
 Whilst the second term multiplied by the same mass describes the vortex force.
 Here ${\vec\omega}=[\nabla\times{\vec{\mathit V}}]$ is named the vorticity.
Obviously, from here it follows that the velocity ${\vec{\mathit V}}$ is represented by superposition
of irrotational and solenoidal components~\citep{KunduCohen2002}.
 The first component stems from the gradient of the scalar field.
While the second component is due to the vector field where the Kelvin-Stokes theorem gives
the rule for calculus of the curl of the vector field over some surface~\citep{Katz1979}.

By applying the curl operator to Eq.~(\ref{eq=33}) we get the equation for the vorticity
\begin{equation}
  {{\partial{\vec\omega}}\over{\partial\,t}}
 + ({\vec\omega}\cdot\nabla){\vec{\mathit V}}
 = \nu(t) \nabla^{\,2}{\vec\omega}.
\label{eq=35}
\end{equation}
 Here $\nu(t) = \mu(t)/(m_{0}\rho)$ is the kinetic viscosity. Its dimension is [length$^2$/time].

 Assuming that the fluid is a physical vacuum, which is superfluid~\citep{Volovik2003}, one says that the viscosity is missing.
 In such a case, the vorticity $\vec\omega$ is concentrated in the point of the origin. Its mathematical representation is a $\delta$-function. This singularity can be a source of possible divergences of computations in later on.

Here we proclaim that the viscosity coefficient, $\nu(t)$,
 accidentally changes sign with the lapse of time.
Let, at that, the average in time  of the coefficient $\nu(t)$ be equal to zero, but its variance stays positive.
Such unusual changes of sign in the viscosity  can mean only that there occurs
 the exchange of the energy of the vortex
 with zero fluctuations of the vacuum~\citep{Sbitnev2015b, Sbitnev2015c}.

 Further we shall consider a simple model of the vortex. Let us look into the vortex tube in its cross-section which is oriented along the $z$-axis  and its center is placed in the coordinate origin of the plane $(x, y)$. Eq.~(\ref{eq=35}), written down in the cross-section of the vortex, is as follows
\begin{equation}
  {{\partial\, {\omega}}\over{\partial\,t}} =
 \nu(\,t\,)\Biggl(
    {{\partial^{\,2}\omega}\over{\partial\,r^{2}}}
 +{{1}\over{r}}{{\partial\,\omega}\over{\partial\,r}}
               \Biggr).
\label{eq=36}
\end{equation}
 The solution of this equation reads
\begin{equation}
   \omega(r,t) =
{{\mit\Gamma}\over{  \Sigma(\,t\,)  }}
\cdot \exp\Biggl\{
  - {{r^2}\over{  \Sigma(\,t\,)  }}
  \Biggr\}
\label{eq=37}
\end{equation}
 and the orbital speed is
\begin{eqnarray}
\nonumber
 {\mathit{ V}}(r,\,t)
&=& {{1}\over{r}}\int\limits_{0}^{r}\omega(r',t)r'dr' \\
&=&  {{\mit\Gamma}\over{2 r}}\Biggl(\!1 -
 \exp{\Biggl\{
   - {{r^2}\over{  \Sigma(\,t\,)  }}
  \Biggr\}}\!
  \Biggr).
\label{eq=38}
\end{eqnarray}
 Here $\mit\Gamma$ is the integration constant having dimension m$^2$/s
 and the denominator $\Sigma(\,t\,)$ reads
\begin{equation}
  \Sigma(\,t\,) = 4 \Biggl( \int\limits_{0}^{t} \nu(\,t'\,)dt' + \sigma^{2} \Biggr)
\label{eq=39}
\end{equation}
 Here $\sigma$ is an arbitrary constant such that the denominator is always positive.
\begin{figure}[htb!]
  \centering
  \begin{picture}(200,125)(22,20)
      \includegraphics[scale=0.75]{Fig01a}
  \end{picture}
  \caption{
  Vorticity $\omega(r)$ and orbital speed ${\mathit V}(r)$  as functions of $r$ at given $t$
  for ${\mit\Gamma}=\pi\cdot10^{-4}$ m$^2$/s, $\nu=\hbar/2m_{0}$ ($m_{0}$ is the electron mass),
 $\Omega=6.58\cdot10^{15}$ s$^{-1}$, and $\sigma=1.914\cdot10^{-10}$ m.
 The  boundary of the core is $r^* \approx 5.29\cdot10^{-11}$ m.
   }
  \label{fig=1}
\end{figure}

 For the sake of simplicity we set
\begin{equation}
  \nu(\,t\,) = \nu\cos(\Omega\,t )
=\nu{{e^{{\bf i}\Omega\,t}+e^{-{\bf i}\Omega\,t}}\over{2}}
\label{eq=40}
\end{equation}
In this case
\begin{equation}
  \Sigma(\,t\,) = 4 ({{\nu}/{\Omega}})\sin(\Omega\,t) + \sigma^{2} .
\label{eq=41}
\end{equation}
Here $\Omega$ is an oscillation frequency and $\nu$ let be equal to $\hbar/2m_{0}$, compare with Eq.~(\ref{eq=6}).
 Behavior of the functions~(\ref{eq=37}) and~(\ref{eq=38})
 calculated for the case of the electron-positron pairs fluctuating on the first Bohr orbit
 are shown in Fig.~\ref{fig=1}.

The functions $\omega(r,t)$ and ${\mathit V}(r,t)$ oscillate about  some average values
 limited by $\sigma$~\citep{Sbitnev2015b, Sbitnev2015c}.
 It looks as the vortex is  pulsating in time, at least pulsating the core's wall
 marked in the figure by the radius $r^{*}$.
 The pulsations are due to the annihilation-creation process of the virtual electron-positron pairs.
\begin{figure}[htb!]
  \centering
  \begin{picture}(200,170)(25,10)
      \includegraphics[scale=0.45]{galaxy}
  \end{picture}
  \caption{
   Vortex's simulation.
  Circle drawn in the center covers an area of the core.
  On edge of the core the orbital speed reaches a maximal value.
  Rotation is shown by arrows.
 The dotted arrow being perpendicular to the rotation plane
 points orientation of the vorticity.
   }
  \label{fig=2}
\end{figure}
\begin{figure}[htb!]
  \centering
  \begin{picture}(200,125)(20,15)
      \includegraphics[scale=0.75]{Fig03a}
  \end{picture}
  \caption{
  Vorticity $\omega(r)$ and orbital speed ${\mathit V}(r)$  as functions of $r$ at given $t$.
 Scaling  units are adopted as stated in~\citep{deBlokEtAl2001}.
   }
  \label{fig=3}
\end{figure}

\section{\label{sect4}Vortex strings and dark matter}

Simulation of the vortex is shown in Fig.~\ref{fig=2}.
Simulating the vortex we choose a two-arm mode in the azimuthal equidistant projection
 because of which the vortex manifests a good spiral form. It looks almost like a galaxy.
 The vortex has a core which does not exceed the radius~$r^{*}$
 where the point of inflection of the orbital velocity ${\mathit V}(r)$ occurs.
 In the figure this area is outlined by a circle with the arrows pointing out the rotation of the matter.
 Below this circle the velocity diminishes and in the core we see agglomeration of the slowly rotating matter.
Above this circle the velocity reaches, at least, its maximal values and stays almost constant.

It is that the stars in the galaxy rotate around the galactic core with almost constant speed even being located far from the galactic core.
Really, the orbital speed of stars and gas, ${\mathit V}$, is rising inside the core and reach almost constant level outside the core~\citep{deBlokEtAl2001}.
The orbital speed can look as shown in Fig.~\ref{fig=3}.

We assume that there is a wide spectrum of the viscosity coefficients.
For the sake of simple presentation we believe that the spectrum is discrete with equidistant position
of each component which has a form
\begin{equation}
  \nu_{\,n}(\,t\,) = {{c^{\,2}}\over{\Omega_{n}}}\cos(\Omega_{n}t).
\label{eq=42}
\end{equation}
Take yourself attention that the coefficient $c^{\,2}/\Omega_{n}$ is fully equivalent to
the diffusion coefficient~(\ref{eq=5}), here $c$ is the light speed.
Also one can see that $c^{\,2}/\Omega_{n}$ submits to the $1/f$-law
that exhibits itself as the flicker-noise (colored noise)~\citep{HanggiJung1995} when $n$ tends to infinity.
Namely, we admit that
\begin{equation}
  \Omega_{n} \sim n^{-\alpha}, ~~~~ \alpha \ge 1.
\label{eq=43}
\end{equation}
It should take into attention here, that the spectrum  is condensed in the point $\Omega = 0$.
In other words, the strongest contribution to the vorticity give modes with frequencies close to zero:
\begin{equation}
 \Sigma_{n}(\,t\,) = 4 \biggl(
  {{c^{\,2}}\over{\Omega_{n}^{2}}}\sin(\Omega_{n}t) + \sigma_{n}^{2}
                                \biggr).
\label{eq=44}
\end{equation}

 The vorticity
\begin{equation}
 \omega(r,t) = {{\mit\Gamma}\over{N}} \sum\limits_{n=1}^{N}
 {{1}\over{ \Sigma_{n}(\,t\,)}}\exp\Biggr\{
                                                                                -{{r^2} \over {\Sigma_{n}(\,t\,)}}
                                                                         \Biggl\}
\label{eq=45}
\end{equation}
 and the orbital speed
\begin{equation}
 {\mathit V}(r,t) = {{\mit\Gamma}\over{2 rN}}
 \sum\limits_{n=1}^{N}
 \Biggr(
 1 -\exp\Biggr\{
                      -{{r^2} \over {\Sigma_{n}(\,t\,)}}
             \Biggl\}
 \Biggl).
\label{eq=46}
\end{equation}
 These curves are calculated   for  choosing
 ${\mit\Gamma} = 10^{27}$~m$^2$/s,
 $\Omega_{n} = 10^{-11}n^{-1}$~s$^{-1}$, and $N=25$. The parameter $\sigma_{n} = 4c/\Omega_{n}$ m
  ranges from 10,000 to 300,000 light years which covers  the diameter of the ordinary spiral galaxy~\citep{Howell2015}.
 This parameter  tends to infinity as $\Omega$ goes to zero.
 It prevents a catastrophe of the barion matter with the course of time.
 The curves are shown in Fig.~\ref{fig=3}.

\begin{figure}[htb!]
  \centering
  \begin{picture}(200,230)(20,10)
      \includegraphics[scale=0.6]{Velocity3D}
  \end{picture}
  \caption{
  Orbital speed ${\mathit V}$  as function of
 the radius $r$ from the galactic center (in kiloparsec)
 and time $t$ (in light years).
   }
  \label{fig=4}
\end{figure}

We have shown that the orbital speed can manifest a roughly flat rotation curve if the vorticity bundles are assembled according to the $1/f$-law. The frequency range in that case stretches from high frequencies belonging to the quantum realm up to about $6\cdot10^{-14}$ Hz.
These ultra-low frequencies, in terms of wavelengths, are covering almost entirely the diameter of the ordinary spiral galaxy, $\lambda=c/{\omega} \approx 5\cdot10^{\,5}$ light years, or about 150 kpc.
In this sense, the formulas~(\ref{eq=45}) and~(\ref{eq=46}) describe thermalization of the vorticity and angular velocities of spiral galaxies as a result of the energy exchange of baryonic matter with the physical vacuum.

Fig.~\ref{eq=4} shows evolution of the orbital speed,~${\mathit V}$, for the time ranging from 100 to 1100 light years. Through the whole time interval the orbital speed keeps its own form. One can see, however, that the curve experiences small fluctuations in  time, resembling the breathing of the galaxy. This breathing is caused by the exchanging energy with the physical vacuum on the ultra-low frequencies owing to the term $\Sigma_{n}(\,t\,)$. It manifests in variations of the vorticity $\omega$.
 On these ultra-low frequencies this exchange occurs by the virtual particle-antiparticle pairs named as  gravitational dipoles~\citep{Hajdukovic2011a, Hajdukovic2011b, Hajdukovic2014a}.
It is believed that such a manifestation stems from dark matter~\citep{Rubin2004}.
But  Hajdukovic writes~\citep{Hajdukovic2011a}: "dark matter does not exist but is an illusion created by the polarization of the quantum vacuum by the gravitational field of the baryonic matter. Hence, for the first time, the quantum vacuum fluctuations, well established in quantum field theory but mainly neglected in astrophysics and cosmology, are related to the problem of dark matter."

The vorticity reaches a maximal value in the center of the vortex core.
We may imagine that the vorticity spreads far from the plane of a spiral galaxy in the transverse direction due to the involvement in the vortex activity of enormous amount of the virtual gravitational dipoles.
Such a direction is shown by dotted arrow in Fig.~\ref{fig=2}.
 It is instructive to recall here the Helmholtz theorems pointing to the certain properties of the vortex:
(i)~the strength of a vortex filament is constant along its length; (ii)~a vortex filament cannot end in a fluid medium; it must form a closed path (like a smoke ring), end at a boundary (solid or free surface), or go to infinity; (iii)~in the absence of rotational external forces, a fluid that is initially irrotational remains irrotational.

One might guess that a substance called as
 the dark matter~\citep{Rubin2004, LaigleEtAl2014, PichonEtAl2014, PichonEtAl2014a} manifests itself through such vortex formations.
As follows from the  Helmholtz theorems they penetrate through the whole universe by creating a complex web of the
vortex filaments.
These formations, thread-like formations, play a role in the centers of condensation of the barion matter along which the galaxies are formed.

\section{\label{sec5}Conclusion}

The equation of the relativistic hydrodynamics, describing motion of the perfect fluid,
plus the continuity equation can be reduced to the relativistic quantum equation, the Klein-Gordon equation,
as soon as the quantum potential is found.
In non-relativistic limit these equations reduce to the Schr\"odinger equation.

The problem of finding the quantum potential
goes back to Fick's  laws written down in the relativistic sector.
A main essence of these laws is that they describe currents induced by gradients of the pressures
arising in a special superfluid medium -  the physical vacuum.
So, the quantum potential describes influence through differences of the pressures
that arise between ensembles of virtual particles populating the vacuum.

The equation of the relativistic hydrodynamics when the viscosity term added gives the possibility of describing vortices arising in such a non-perfect fluid.
We proclaim in that regard that averaged in time the viscosity coefficient vanishes, but its dispersion is not zero.
Due to this trick, the vortex can live infinitely long and the vortex radius trembles.
The trembling is due to the exchange of the vortex energy with the zero-point vacuum fluctuations.
Note that, the vortex has non-zero radius of the core where the vortex speed tends to zero.

Consideration of the rotating motion of the spiral galaxy through a prism of the hydrodynamical equation loaded by the viscosity fluctuating about zero gives explanation for observed flattening of the orbital speeds on radii far exceeding the radius of the galactic core. Exchange of the energy of the rotating galactic matter with the zero-point fluctuations of the physical vacuum on ultra-low frequencies, that is, the exchanging by means of gravitational quanta, induces effect that looks as a breathing of the galaxy. Contribution of the ultra-low frequencies showing the distribution like the flicker noise law,  $1/f$, provides flattening the orbital speeds on the large radii.

The zero-point vacuum fluctuations on the ulta-low frequencies can explain observed flattening of the orbital speeds of the spiral galaxies without attracting the idea of dark matter.

The Helmholtz theorem says that any vortex tube is continued in the space until it reaches a boundary of the space or the tube is closed on its own ends by forming a torus. It means that the vorticity in large-scale supports existence of the cosmic filaments. As observation shows, the cosmic filaments form a complicated web~\citep{LaigleEtAl2014, PichonEtAl2014, PichonEtAl2014a}. One may guess that this complicated web can be the result of turbulent mixing of the vortices. We know from the hydrodynamics, that the hydrodynamic equations contain a rich set of solutions. Among all of these, turbulent solutions represent a special class which is attracting attention by its variety of forms.

\begin{acknowledgments}

 The author thanks
 Mike Cavedon,  Pat Noland, and Denise Puglia
  for  valuable remarks and propositions.

\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


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MANILA, Philippines – Interior Secretary Eduardo Año on Thursday welcomed the petition filed by the Alliance of Concerned Teachers (ACT) before the Court of Appeals (CA) to stop the police from profiling its members.
In its petition through the National Union of People's Lawyers, ACT asked the CA to issue a restraining order against the intelligence gathering of the Philippine National Police (PNP) aimed at identifying its members who may supporting the communist movement.
"The DILG (Department of the Interior and Local Government) and the PNP welcome the case filed, a petition for prohibition, by the ACT before the Court of Appeals," Año said in a statement.
But despite welcoming the move of the party-list group, Año denied that the PNP had violated any of the rights of ACT as it claimed in the petition.
He said that intelligence gathering is a task routinely conducted by law enforcement agencies, and noted that Communist Party of the Philippines founder Jose Maria Sison himself tagged ACT as one of its legal fronts.
"The PNP will be guilty of dereliction of duty and negligence if it were to do nothing about Sison's admission that is making the rounds of social media," Año said.


Look ravishing in Clarisse 3538. Deep V-neckline is secured with sheer inset at center front. Low V-back bares enough skin to make it more flattering. Floral prints showered the pleated ball skirt giving the dress a daintier appeal.


text:
package dk.brics.tajs.analysis;

/**
 * Descriptors for the APIs implemented in the analyzer.
 */
public enum NativeAPIs {

	ECMA_SCRIPT_NATIVE ("ECMAScript native functions"),
	DOCUMENT_OBJECT_MODEL ("The Document Object Model");

	private String s;

	private NativeAPIs(String s) {
		this.s = s;
	}

	@Override
	public String toString() {
		return s;
	}
}

redpajama_set_name: RedPajamaGithub


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Swifts may have gotten the better of Taylors Lake on the football field and netball court on Saturday, but both clubs came together as one to celebrate their annual Indigenous round. Sonny and John Secombe led a pre-game dance before the senior contest, sharing their culture with those in attendance. Both teams donned specially designed guernseys with Indigenous designs, while Swifts flew Aboriginal and Torres Strait Island flags as well as painting the Indigenous flag on the ground. READ MORE: Baggies overcome Lakers challenge Sonny Secombe said it was great to see the occasion embraced for another year. "Both clubs really look forward to it, regardless of the result either way," he said. "The community really gets involved and it adds that element of culture. It is great to put it in that sporting context and it's a great achievement by the clubs who have taken the initiative to set the footprint for the league." READ MORE: Swifts finals bound Swifts coach Scott Carey said it was special to be part of the occasion once again. "The two clubs have worked hard to keep driving it for four years now, it is a credit to everyone involved who makes it happen," he said. "We, just like Taylors Lake, have had a lot of great aboriginal clubmen and it is great to show some appreciation back with a day like this." While you're with us, you can now receive updates straight to your inbox each Friday morning from the Stawell Times-News. To make sure you're up-to-date with all the news from across the Northern Grampians shire, sign up here.
/images/transform/v1/crop/frm/lachlan.williams/5eb68fdb-1b91-4428-a653-309d13993b40.JPG/r0_88_5184_3017_w1200_h678_fmax.jpg
July 27 2019 - 9:00PM
Lakers, Swifts celebrate Indigenous culture with annual contest | Photos
Swifts may have gotten the better of Taylors Lake on the football field and netball court on Saturday, but both clubs came together as one to celebrate their annual Indigenous round.
Sonny and John Secombe led a pre-game dance before the senior contest, sharing their culture with those in attendance.
Both teams donned specially designed guernseys with Indigenous designs, while Swifts flew Aboriginal and Torres Strait Island flags as well as painting the Indigenous flag on the ground.
READ MORE: Baggies overcome Lakers challenge
Sonny Secombe said it was great to see the occasion embraced for another year.
"Both clubs really look forward to it, regardless of the result either way," he said.
"The community really gets involved and it adds that element of culture. It is great to put it in that sporting context and it's a great achievement by the clubs who have taken the initiative to set the footprint for the league."
READ MORE: Swifts finals bound
Swifts coach Scott Carey said it was special to be part of the occasion once again.
"The two clubs have worked hard to keep driving it for four years now, it is a credit to everyone involved who makes it happen," he said.
"We, just like Taylors Lake, have had a lot of great aboriginal clubmen and it is great to show some appreciation back with a day like this."
While you're with us, you can now receive updates straight to your inbox each Friday morning from the Stawell Times-News. To make sure you're up-to-date with all the news from across the Northern Grampians shire, sign up here.

redpajama_set_name: RedPajamaCommonCrawl


Arri is very athletic for a race that has to this point, lived onboard a refugee fleet. Due to the Alindari's extended exposure to artificial gravity, they thrive in 0.5 Gs. Also their muscle density is lower, and because of this, Arri must undertake a daily physical regiment in order to function in a 1 G environment.


Árpád Bogdán's new film provides a dramatic depiction of sin, catharsis and rebirth. The story of Genesis is formed around the fate of a young Roma boy, whose childhood reaches a sudden and drastic end when he loses his family in a tragic and brutal attack. Already buried in her work, a young female lawyer succumbs to pressure from her superior and undertakes the defence of one of the men facing trial for the part he reputedly played in this infamous series of racist murders. It is while researching the case that she comes into contact with the young boy, called as a witness, and this chance meeting changes both their lives forever. A mysterious teenage girl also becomes involved when her boyfriend's dark secrets come to light.
With strong biblical roots, the story is told via the journeys of very different individuals from completely separate sections of society whose paths never cross but whose fates become intricately entwined as they twist through the shadow cast by this horrendous crime.
The protagonists in Genesis decide their various fates based on the universal human values of faith in life, solidarity and responsibility, and each is then presented with the chance of a new beginning, a new life.


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SDGs office denies inserting N33bn allocation in budget
The Office of the Senior Special Assistant to the President on Sustainable Development Goals on Friday refuted claims of inserting N33bn as additional allocation for the agency in the 2020 budget.
It said in a statement issued in Abuja that the said amount or any other allocation aside from the duly appropriated figure was not known to the SDG office.
"The office also wishes to state that aside from the opportunity to defend its budget proposal before the relevant committees at the National Assembly as prerequisites for the passage of budget, the Office of the Senior Special Assistant to the President on SDGs has no power whatsoever over the review of the budgetary proposal," the office stated.
It noted that the responsibility of the office over the years had been limited to implementing the budget as duly approved and signed by the President, subject to the release of funds appropriated for the different sub-heads.
The SDG office said the insinuation was an attempt to drag it into unnecessary controversies.


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Clogher Mart: Beef cows sell to a top of £1,636.20
A larger entry of 870 cattle on offer sold to much stronger demand at Clogher Mart last week in all sections.
In the fatstock ring beef cows sold to a top of £1,636.20 for an 810kg Belgian Blue at £202 per 100kg followed by an 830kg Limousin at £185 to total £1,535.50.
Cow heifers topped £1,320 for a 670kg Limousin at £197 per 100kg followed by a 680kg Simmental at £188 per 100kg to total £1,278.40.
Fleshy Friesian cows sold to £132 per 100kg.
Fat bulls sold to £1,642.80 for a 1,110kg Limousin at £148 selling to a top of £152 per 100kg for a 960kg Charolais (£1,459.20).
Leading prices in the fatstock ring for beef cows and heifers as follows: Other quality lots sold from £140 to £172 per 100kg.
Second quality lots sold from £115 to £137 per 100kg.
Well fleshed Friesian cows sold from £124 to £132 per 100kg.
Plainer lots sold from £84 to £119 per 100kg.
Poorer types sold from £56 to £78 per 100kg.
FAT BULLS
Fivemiletown producer 960kg Charolais to £152 (£1,459.20), Dromore producer 1,110kg Limousin to £148 (£1,642.80), Newmills producer 900kg Charolais to £145. Galbally producer 770kg Limousin to £145. Kinawley producer 890kg Limousin to £142. Moy producer 1,000kg Charolais to £139. Ballinamallard producer 970kg Charolais to £133. Hillsborough producer 990kg Hereford to £114. Newtownbutler producer 890kg Aberdeen Angus to £114.
FAT STEERS OVERAGE
Draperstown Mart (Richard Beattie): Bullocks sell to £1,400 for 680kg
630kg Limousin to £188. 730kg Charolais to £181. 780kg Charolais to £177. 660kg Limousin to £174. 590kg Charolais to £172. 630kg Simmental to £170. 560kg Limousin to £165.
FAT STEERS UNDERAGE
790kg Blonde d'Aquitaine to £182. 500kg Simmental to £178. 840kg Charolais to £172. 730kg Hereford to £170. 630kg Hereford to £170. 600kg Hereford to £172 twice, 590kg Shorthorn dairy to £156. 460kg Swedish Red to £149. 560kg Friesian to £149. 600kg Friesian to £149. 460kg Holstein to £133.
FAT HEIFERS UNDERAGE
430kg Limousin to £204. 680kg Simmental to £196. 560kg Charolais to £194. 510kg Charolais to £183. 690kg Simmental to £182. 600kg Aberdeen Angus to £181. 400kg Limousin to £176. 600kg Limousin to £166. 430kg Aberdeen Angus to £158. 510kg Shorthorn beef to £152. 480kg Holstein to £142. 520kg Friesian to £138.
STORE BULLOCKS (111)
A very firm demand in this section with forward lots selling to £1,435 for a 670kg Limousin (£214), 650kg Limousin to £1,415 (£217), 640kg Limousin to £1,370 (£214), 630kg Limousins to £1300 each (£206) for G Johnston, Stewartstown, P Connelly, Fintona 590kg Charolais to £1,285 (£217), 610kg Simmental to £1,280, 620kg Charolais to £1,280, 570kg Charolais to £1,230 (£215) and 580kg Charolais to £1,225. P McMeel, Augher 630kg Simmental to £1,260 and 570kg Charolais to £1,150. E McCaffery, Tempo 560kg Charolais to £1,185, 560kg Charolais to £1,135 and 560kg Charolais to £1,120. Geo Hobson, Portadown 560kg Blonde d'Aquitaine to £1,180, 560kg Limousin to £1,110 and 570kg Charolais to £1,100. J D Noble, Fivemiletown 550kg Aberdeen Angus to £1,150. S Kelly, Loughgall 530kg Aberdeen Angus to £1,100.
MEDIUM WEIGHT STORES 410KG TO 500KG
E O'Neill, Cabra 490kg Limousin to £1,190 (£243) and 460kg Limousin to £990. E McCaffery, Tempo 500kg Aberdeen Angus to £1,095 (£219), 480kg Charolais to £1,035, 490kg Charolais to £1,015, 480kg Charolais £1,015 and 470kg Charolais to £940. Beragh producer 470kg Charolais to £1,000, S Kelly, Loughgall 430kg Charolais to £990 (£230), 470kg Charolais to £950, 410kg Charolais to £950 (£231) and 420kg Charolais to £920. J D Noble, Fivemiletown 450kg Aberdeen Angus to £940. A Gordon, Fivemiletown 460kg Aberdeen Angus to £935. Downpatrick producer 460kg Belgian Blue to £935. P Mallon, Dungannon 480kg Belgian Blue to £930 and 470kg Aberdeen Angus to £900. R Canavan, Coalisland 480kg Aberdeen Angus to £925. J Foster, Armagh 480kg Limousin to £900.
SMALLER SORTS 400KG & UNDER
M Devine, Castlederg 340kg Belgian Blue to £700. J Courtney, Dungannon 320kg Shorthorn beef to £500.
STORE HEIFERS (120)
Great demand in this section with forward lots selling to £1,590 for a 710kg Limousin (£224) for D G Green and Sons, Lisburn. W S Hall, Magheraveely 620kg Charolais to £1,400 (£226), 640kg Charolais to £1,340 (£209), 620kkg Charolais to £1,340 (£216), 610kg Charolais to £1,310 (£215), 600kg Charolais to £1,280 (£213), 580kg Charolais to £1,285 (£221.50), 570kg Charolais to £1,220 (£214), B D Breen, Eskra 620kg Limousin to £1,325. K McManus, Carrowmacken 600kg Charolais to £1,290 (£213), 570kg Charolais to £1,275 (£223), V and S Sommerville, Ballinamallard 550kg Limousin to £1,275 (£232) and 550kg Limousin to £1,255 (£228), J R Shaw, Maguiresbridge 620kg Simmental to £1,270 and 580kg Charolais to £1,230. G Reid, Armagh 600kg Limousin to £1,200. H McClure, Fivemiletown 570kg Charolais to £1,200. W R Adams, Fivemiletown 540kg Belgian Blue to £1,200 (£222) and P J Corrigan, Dungannon 580kg Charolais to £1,200.
H McClure, Fivemiletown 500kg Charolais to £1,140 (£228), 490kg Charolais to £1,065, 480kg Charolais to £1,040, 460kg Charolais to £1,035 (£225) and 480kg Charolais to £990. C Boyle, Armagh 470kg Limousin to £1,140 (£242.50), 480kg Limousin to £1,080 and 460kg Limousin to £970. G Johnston, Stewartstown 500kg Limousin to £1,100 (£220), J R Shaw, Maguiresbridge 500kg Hereford to £1,000 (£200), A Gordon, Fivemiletown 450kg Aberdeen Angus to £985 (£219) and 460kg Aberdeen Angus to £970 (£211), G Reid, Armagh 470kg Limousin to £970. S Maguire, Maguiresbridge 440kg Limousin to £920 and 410kg Limousin to £880. P McGirr, Ballygawley 420kg Limousin to £890.
S Maguire, Maguiresbridge 380kg Limousin to £820. C and D Connelly, Newtownbutler 350kg Charolais to £800, 370kg Charolais to £780, 390kg Charolais to £710. B Quinn, Dungannon 390kg Belgian Blue to £685 and 370kg Belgian Blue to £575. P Tally, Dungannon 310kg Limousin to £610 and 290kg Limousin to £560.
WEANLINGS
Very strong demand in this section with steers and bulls selling to £1,160 for a 500kg Charolais (£232), 510kg Limousin to £1,140 (£223) 460kg Limousin to £1,135 (£247) and 370kg Limousin to £995 (£269) for J McSorley, Beragh. J Mackle, Moy 530kg Charolais to £1,100, 540kg Charolais to £1,075 and 510kg Charolais to £975. B L Kelly and Sons, Dungannon 460kg Charolais to £1,060 (£230), A Short, Omagh 420kg Limousin to £1,060, 420kg Limousin to £1,045 and 420kg Limousin to £960. S McConnell, Clogher 450kg Charolais to £1,035. D Williamson, Fivemiletown 390kg Limousin to £985. P Montgomery, Augher 420kg Charolais to £965 and 370kg Limousin to £930. E Kelly, Augher 340kg Limousin to £965 (£284), E McBride, Ballygawley 440kg Charolais to £950 and 400kg Charolais to £950. G Litter, Portadown 420kg Limousin to £940. M Gormley, Omagh 380kg Charolais to £940.
WEANLING HEIFERS
R E Wilson, Trillick 340kg Limousin to £930 (£273), 380kg Limousin to £835, 390kg Limousin to £775 and 350kg Limousin to £770. P Montgomery, Augher 370kg Limousin to £895 and 410kg Limousin to £895. E Kelly, Augher 340kg Limousin to £870. J Mackle, Moy 420kg Charolais to £865. B Holland, Dungannon 430kg Aberdeen Angus to £860 and 470kg Aberdeen Angus to £840. Jonathan Keys, Clogher 360kg Simmental to £825. E Cassidy, Tempo 360kg Charolais to £820. Kesh producer 320kg Limousin to £805. K Lavery, Lurgan 380kg Aberdeen Angus to £770. F McKenna, Augher 360kg Limousin to £740. J Rea, Crumlin 330kg Charolais to £735. C Maguire, Brookeborough 330kg Limousin to £730.
DAIRY COWS & HEIFERS
A smaller entry last wek sold to £1,500 and £1,300 for calved heifers from a Fivemiletown producer. C Anderson, Dungannon £1,440 for calved heifer. H Rainey, Ballygawley £1,410 for calved heifer. S Mullan, Beragh £1,280 for calved heifer. A Wright, Dungannon £1,280 for springing Shorthorn bred heifer. A selection of maiden heifers sold from £490 to £665.
SUCKLER COWS & CALVES
A much larger entry this week sold to a steady demand for quality lots with plainer lots harder to clear. C Taggart, Fintona sold a third calver and bull calf to £1,905, heifer and heifer calf to £1,615 and second calver and bull calf to £1,500. T McKay, Banbridge £1,800 for 2012 cow and bull calf £1,355 and £1,300 for heifers with heifer calves. I A Elliott, Blaney £1,700 for heifer with bull calf. Martin Rafferty, Dungannon £1,660 for heifer and heifer calf and £1,640 for heifer and bull calf. T W Cashel, Tempo £1,555 for heifer and heifer calf. P and S McNally, Cookstown £1,550 for heifer and bull calf and £1,420 for heifer and heifer calf. E Stewart, Fivemiletown £1,405 for second calver and bull calf. D Tumelty, Downpatrick £1,330 for heifer and heifer calf. T Pennell, Lisnaskea £1,310 for heifer and bull calf. Lots of other outfits sold from £900 top £1,270. A selection of incalf heifers from Pat Cassidy, Augher sold from £1,050 to £1,250.
DROPPED CALVES & REARED CALVES
A smaller entry sold to a brisk demand with bull calves (under two months) selling to £550 for a Charolais to D McCrystal, Ballygawley. William Wilson, Dungannon £485 for Simmental. J Teague, Dromore £465 for Charolauis. C Donaghy, Carrickmore £420 for Limousin. P McGirr, Ballygawley £405 for Limousin. D E L Nelson, Maguiresbridge £380 for Charolais. D Hoey, Maguiresbridge £360 for Limousin. D J Barbour, Lisbellaw £350 for Charolais. K Brannigan, Dungannon £340 for Aberdeen Angus.
HEIFER CALVES
W Hall, Dungannon £400 for Charolais. D McCrystal, Ballygawley £395 for Limousin and £285 for Aberdeen Angus. D Murray, Fintona £300 for Limousin. L G Collins, Lisnaskea £280 for Hereford. P McCorry, Derrylin £265 for Belgian Blue.
REARED BULLS
B O'Neill, Dungannon £775 for Limousin. A W Wilson, Dungannon £705 for Charolais, A Johnston, Omagh £700 for Blonde d'Aquitaine. E and P Hughes, Augher £555 for Charolais. William Wilson, Dungannon £450 for Charolais and £435 for Limousin. J Scott, Maguiresbridge £450 for Hereford. J W McFarland, Trillick £445 and £435 for Limousins. R Dane, Lisbellaw £430, £415, £390 and £365 for Aberdeen Angus. E P Hughes, Augher £430 for Aberdeen Angus.
REARED HEIFERS
R Douglas, Portadown £625 for Charolais. Jonathan Keys, Clogher £600 for Saler, £590 and £500 for Charolais with £590 twice and £580 for Limousins. J P Trimble, Lisbellaw £410 for Limousin. J Donnelly, Trillick £395 for Limousin J Scott, Maguiresbridge £390 for Charolais. K Brannigan, Dungannon £330 for Charolais. William Wilson, Dungannon £325 for Limousin. R Dane, Lisbellaw £310 and £300 twice for Aberdeen Angus.
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Home » Will end of women's driving ban put Saudi Arabia on the right road?
Will end of women's driving ban put Saudi Arabia on the right road?
Saudi Arabia on 24 June lifted its driving ban on women, as it tries to get more females into the workforce; but it has also cracked down on women's rights activists who campaigned against the ban. So how deep do the kingdom's much-vaunted reforms of women's rights actually go, and what do they mean for foreign businesses and expat women in Saudi Arabia?
Saudi Arabia lifted its ban on women driving on 24 June, 2018
• 2001: Women are permitted personal ID cards, although issued to their male 'guardians'.
• 2005: Forced marriage is criminalised. However, marriage contracts continue to be drawn up between the husband and father of the bride.
• 2011: Women are given the right to vote.
• 2013: Women are allowed to ride bicycles and motorcycles in recreational areas. However, they must adhere to full Islamic dress and have a guardian present.
• 2015: Women are allowed to stand in municipal elections.
• 2017: Women make up an estimated 30 percent of the private sector workforce in Saudi Arabia – an increase of 130 percent increase in four years.
• 12 January 2018: Women are permitted to enter sports stadiums to watch events featuring male players. However, they must be segregated from male-only crowd areas and sit within a family section.
• 24 June 2018: The ban on women driving in Saudi Arabia is lifted.
Women's rights to benefit the economy
Saudi Arabia is a rentier state with around 50 percent of its GDP derived from the oil and gas sector. Under the leadership of Crown Prince Mohammad bin Salman – known colloquially as MbS –the Saudi government is advancing an agenda of economic and social reform. Here, Saudi's Vision 2030 and the National Transformation Plan aim to revive the country's non-oil economy. Such ambitions include: doubling the real estate sector's percentage of GDP from 5 to 10 percent by 2020; an increase in household spending on cultural and entertainment activities from 2.9 to 6 percent of GDP; an increase in the private sector's contribution of GDP from 40 to 65 percent; and an increase in foreign direct investment from 3.8 to 5.7 percent of GDP.
Within this continuum of reform and economic advancement, Saudi women are gaining social freedoms. This is because MbS aims to tap into Saudi Arabia's significantly underused female workforce in order to benefit the wider economy. While Saudi Arabia currently has the largest gender imbalance in the labour participation rate among G20 countries, Vision 2030 aims to increase overall female labour force participation . Understanding the need for female labour force participation in order to advance the socio-economic position of Saudi Arabia, Salman aims to address factors currently influencing the exclusion of women from the labour market.
Saudi women have been largely excluded from joining the nation's workforce. While the percentage of women in the private sector has increased in recent years – women now make up 30 per cent of its workforce – overall, women still face high levels of exclusion due, in part, to high levels of education centred on skills that are not in demand.
Moreover, women have faced obstacles in gaining employment due to morality laws enforcing segregation in the workplace. Both the public and private sector require the permission of a woman's male guardian in order to hire her, while strict gender segregation in the past limited the ability of small businesses to hire women in the first place, due to the cost of running a separate office.
The restrictions of the male guardianship system extends to travel, as women require their guardian's permission to travel, and companies may be put off hiring women who may face travel obstacles in carrying out job requirements.
Increasing women's access to labour market
In recent years however, the authorities have introduced some reforms in an attempt to increase women's access to the labour market. These include reforming the labour law, which previously restricted women's right to work in fields that were 'unsuitable to their nature', and no longer requiring that women need permission from their guardians to work. Moreover, some work placements do not require complete gender segregation; however a separate break room is still required.
Perhaps the most significant reform is the lifting of the ban on women driving, which came into effect on 24 June 2018. Now women will no longer have to rely on taxis, drivers, or husbands and male relatives in order to commute to work. Moreover, the possibility of female taxi drivers could further open up opportunities for women from conservative backgrounds who are forbidden from using conventional taxis as they are driven by 'unfamiliar men'.
The lifting of the ban could save households around 1,000 USD per month in taxi and personal driver fees. Furthermore, it has been estimated that the move to allow women to drive will help keep 30 billion SAR (8 billion USD) inside the local economy per annum. This would be partly due to Saudi families having increased disposable income as more women work. Another factor would be a fall in numbers of expatriate workers – much of whose salaries are usually spent in their home country – following a 'Saudization' drive reserving some occupations for locals.
Impact of reforms on Saudi women
While the lifting of the driving ban is a historic event for women's rights in Saudi Arabia, women face significant challenges in accessing their right to drive. In addition to the limited number of driving schools, women pay around six time as much as men for lessons. Moreover, in the wake of women being allowed to drive, leading women's rights activists and those who have campaigned against the driving ban have been detained. While Salman is promoted as a reformist championing women's rights in Saudi Arabia, simultaneously the state is cracking down on female activists. This duality indicates a state policy of handing women some rights in order to benefit the economy, while continuing state policy of political repression.
While the guardianship system remains in place, women's ability to participate in the labour market will be greatly limited
Allowing women to drive will have some impact on female participation in the workforce due to greater ease of access to job opportunities for women. However, it is unlikely that this repeal alone will result in mass female participation in the workforce. This is because women will still be affected by Saudi Arabia's guardianship system. Here, women's economic opportunities are largely dependent on the opinions of their male relatives. While more liberal families may allow their daughters to study abroad and take leading roles in business, others may be explicitly forbidden from leaving the house and working. One Saudi recruitment firm reported that an estimated 4 out of 10 women for whom its secures work leave after a few months due to pressure from their families. Therefore, while the guardianship system remains in place, women's ability to participate in the labour market will be greatly limited.
Impact of reforms on foreign companies
It is likely that the increase of Saudi women entering the workplace will have a positive impact on foreign companies with offices in Saudi Arabia. The recent relaxation of complete gender segregation in some workplaces means that companies may not need to secure extra office space to accommodate female staff – although a separate break room for women is still required. Meanwhile, the introduction of local female staff can have a positive impact on an organisation through the fresh insight and ideas they can bring.
The increase in domestic female participation in the workforce may lead to a reduction in Saudi reliance on the expatriate workforce
On a practical level, businesses in the kingdom will have to turn more to locals for staff as reforms to free up employment opportunities to Saudi nationals impact on the expatriate workforce. Currently, more than 11.1 million foreigners work in the private sector, accompanied by more than 2,220,000 relatives. However it has been estimated that around 165,000 expatriate workers will leave by the end of 2018. An array of factors have made Saudi Arabia less attractive to some expats, particularly in blue-collar occupations. These include: a Saudization policy which makes certain jobs, largely in sales and services, reserved for Saudi citizens; an annual tax increase and additional fees for expats' dependants; rises in living costs which are not offset for expats by state subsidies on utilities; and a monthly tax imposed on hiring expats, introduced in 2017.
It is plausible to assume that the increase in domestic female participation in the workforce may lead to a reduction in Saudi reliance on the expatriate workforce.
Impact of reforms on expat women
However, while this era of reform is making life more difficult for expats in general – especially in blue-collar occupations – it will likely create a more comfortable environment for female expat personnel and female business travellers.
In addition to now being able to drive in the kingdom, female expats will also benefit from further social and leisure reforms. These include: the opening of cinemas; the development of a 'semi-autonomous' luxury resort on the Red Sea coast due to open in 2020, which reportedly will be a visa-free travel destination that won't function under Sharia laws; and the opening of an 'entertainment city' in the capital Riyadh. Such social openings may pave the way for a more tolerant society and consequently could create a more relaxed workplace environment in terms of gender segregation.
Another reform that will positively impact the lives of female expats is the new provision for women living in Saudi Arabia to be able to start a business without the permission of their guardian. This could likely give women more business freedom and encourage the development of specifically women-friendly services. However, the provision of this reform is itself limited as women are still often required to provide character references from men before they are granted licences or loans.
Female business travellers are perhaps best impacted by the reforms, as they will likely see the greater freedoms for women in society and within the workplace while not being exposed to growing employment competition from locals that expat personnel are likely to face.
The lifting of the driving ban in Saudi Arabia is part of the government's drive for economic reform. Recognising the economic benefit of female participation in the workforce, Salman has provided a window for social reform in Saudi Arabia. However, it must be stated that such policies are based on economic advancement and the overall benefits to women are limited. This is evident through the continuation of political repression and the guardianship system.
The repeal of the ban on women driving will certainly impact expatriate women workers in a positive way, as will social reforms liberalising entertainment, and measures allowing women to start their own businesses. Moreover, it is plausible that such reforms will be reflected by a less conservative working environment.
Offsetting this, the extension of policies such as Saudization is likely to reduce opportunities for expats in general, as the authorities seek to increase the local composition of the kingdom's workforce.


It was September 11, 2001. I was a route sales supervisor for Mister Bee Potato Chips. I was training a new route salesman. We walked into Kanaha City Krogerand everyone was listening in the backroom on the radio.
It was stunning. They told me an airplane had hit The Twin Towers. This immediately made me concerned. My brother lived just blocks away from the Twin Towers and worked right by it. I had just walked from his apartment to The Towers the year before. I tried to call him and could not get ahold of him. We did not have a radio in the truck.
Our next stop was Marmet Kroger. Again, Kroger employees were listening. By then, it was obvious it was terrorism. As we continued on our route, each store got emptier and quieter and eventually they started shutting down. It was a weird day I'll never forget and it links me forever with Mister Bee.
I was talking to my mom and my friend Becky on the phone as the day unfolded. It took a couple of hours for my mom to make contact with my brother.
That evening was the strangest evening ever...even the major television networks signed off of the air. The country was scared and sad...but it pulled us together as a nation. Even though it broke our hearts, it was the single most unifying event I had ever seen.
For several nights, people did not go out. They stayed at home with their families and were traditional families again. I do not think it was as much fright as just realizing what was important. It made us remember our good old American values as God, family, and work.
I sat over at the old Davis' Place in Huntington a few nights because my friend Becky was a bartender there. There were very few customers do I stayed there with her.
It was the saddest time in our country in my lifetime but it brought us together and brought back patriotism. We had American pride.


Arsenal manager Arsene Wenger is now the longest serving manager in Europe after Ronnie McFall brought his incredible 29-year stay in charge of Portadown to an end - leaving Arsene Wenger as the longest-serving manager in European football.
McFall, who was set to leave the club at the end of the season, resigned minutes after his side's shock Irish Cup quarter-final defeat to Championship outfit Lurgan Celtic.
The 69-year-old took charge at Portadown in December 1986 - the same year Sir Alex Ferguson took over at Manchester United.
Ferguson stepped down at Old Trafford in 2013, leaving McFall as the longest-serving manager in Europe until his decision to step down on Saturday.
That honour now belongs to Wenger, who has been at the helm at Arsenal since October 1996 and is in his 20th year as Gunners boss.