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Register a new userVacuum solutions in the Einstein-Aether Theory
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The Einstein-Aether (EA) theory belongs to a class of modified gravity theories characterized by the introduction of a time-like unit vector field, called aether. In this scenario, a preferred frame arises as a natural consequence of a broken Lorentz invariance. In the present work we have obtained and analyzed some exact solutions allowed by this theory for two particular cases of perfect fluid, both with Friedmann-Lemaitre-Robertson-Walker (FLRW) symmetry: (i) a fluid with constant energy density ($p=-rho_0$), and (ii) a fluid with zero energy density ($rho_0=0$), corresponding to the vacuum solution with and without cosmological constant ($Lambda$), respectively. Our solutions show that the EA and GR theories do not differentiate each other only by the coupling constants. This difference is clearly shown because of the existence of singularities that there are not in GR theory. This characteristic appears in the solutions with $p=-rho_0$ as well as with $rho_0=0$, where this last one depends only on the aether field. Besides, we consider the term of the EA theory in the Raychaudhuri equation and discuss the meaning of the strong energy condition in this scenario and found that this depends on aether field. The solutions admit an expanding or contracting system. A bounce, a singular, a constant and an accelerated expansion solutions were also obtained, exhibiting the richness of the EA theory from the dynamic point of view of a collapsing system or of a cosmological model. The analysis of energy conditions, considering an effective fluid shows that the term of the aether contributes significantly for the accelerated expansion of the system for the case in which the energy density is constant. On the other hand, for the vacuum case ($rho_0=0$), the energy conditions are all satisfied for the aether fluid.
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We study spherically symmetric spacetimes in Einstein-aether theory in three different coordinate systems, the isotropic, Painlev`e-Gullstrand, and Schwarzschild coordinates, in which the aether is always comoving, and present both time-dependent and time-independent exact vacuum solutions. In particular, in the isotropic coordinates we find a class of exact static solutions characterized by a single parameter $c_{14}$ in closed forms, which satisfies all the current observational constraints of the theory, and reduces to the Schwarzschild vacuum black hole solution in the decoupling limit ($c_{14} = 0$). However, as long as $c_{14} ot= 0$, a marginally trapped throat with a finite non-zero radius always exists, and in one side of it the spacetime is asymptotically flat, while in the other side the spacetime becomes singular within a finite proper distance from the throat, although the geometric area is infinitely large at the singularity. Moreover, the singularity is a strong and spacetime curvature singularity, at which both of the Ricci and Kretschmann scalars become infinitely large.
In this work we present all the possible solutions for a static cylindrical symmetric spacetime in the Einstein-Aether (EA) theory. As far as we know, this is the first work in the literature that considers cylindrically symmetric solutions in the theory of EA. One of these solutions is the generalization in EA theory of the Levi-Civita (LC) spacetime in General Relativity (GR) theory. We have shown that this generalized LC solution has unusual geodesic properties, depending on the parameter $c_{14}$ of the aether field. The circular geodesics are the same of the GR theory, no matter the values of $c_{14}$. However, the radial and $z$ direction geodesics are allowed only for certain values of $sigma$ and $c_{14}$. The $z$ direction geodesics are restricted to an interval of $sigma$ different from those predicted by the GR and the radial geodesics show that the motion is confined between the origin and a maximum radius. The latter is not affected by the aether field but the velocity and acceleration of the test particles are Besides, for $0leqsigma<1/2$, when the cylindrical symmetry is preserved, this spacetime is singular at the axis $r=0$, although for $sigma>1/2$ exists interval of $c_{14}$ where the spacetime is not singular, which is completely different from that one obtained with the GR theory, where the axis $r=0$ is always singular.
In the present work we analyze all the possible spherically symmetric exterior vacuum solutions allowed by the Einstein-Aether theory with static aether. We show that there are four classes of solutions corresponding to different values of a combination of the free parameters, $c_{14}=c_1+c_4$, which are: $ 0 < c_{14}<2$, $c_{14} < 0$, $c_{14}=2$ and $c_{14}=0$. We present explicit analytical solutions for $c_{14}=3/2, 16/9, 48/25, -16, 2$ and $0$. The first case has some pathological behavior, while the rest have all singularities at $r=0$ and are asymptotically flat spacetimes. For the solutions $c_{14}=16/9, 48/25, mathrm{, and ,}, -16$ we show that there exist no horizons, neither Killing nor universal horizon, thus we have naked singularities. Finally, the solution for $c_{14}=2$ has a metric component as an arbitrary function of radial coordinate, when it is chosen to be the same as in the Schwarzschild case, we have a physical singularity at finite radius, besides the one at $r=0$. This characteristic is completely different from General Relativity.
We perform numerical simulations of gravitational collapse in Einstein-aether theory. We find that under certain conditions, the collapse results in the temporary formation of a white hole horizon.
How do the global properties of a Lorentzian manifold change when endowed with a vector field? This interesting question is tackled in this paper within the framework of Einstein-Aether (EA) theory which has the most general diffeomorphism-invariant action involving a spacetime metric and a vector field. After classifying all the possible nine vacuum solutions with and without cosmological constant in Friedmann-Lema{^{i}}tre-Robertson-Walker (FLRW) cosmology, we show that there exist three singular solutions in the EA theory which are not singular in the General Relativity (GR), all of them for $k=-1$, and another singular solution for $k=1$ in EA theory which does not exist in GR. This result is cross-verified by showing the focusing of timelike geodesics using the Raychaudhuri equation. These new singular solutions show that GR and EA theories can be completely different, even for the FLRW solutions when we go beyond flat geometry ($k=0$). In fact, they have different global structures. In the case where $Lambda=0$ ($k=pm 1$) the vector field defining the preferred direction is the unique source of the curvature.
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