Abstract
We analyze all the possible spherically symmetric exterior vacuum solutions allowed by the Einstein–Aether theory with static aether. We show that there are three 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, and c_{14}=0. We present explicit analytical solutions for c_{14}=3/2, 16/9, 48/25, -16 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 horizon nor universal horizon, thus we have naked singularities. This characteristic is completely different from general relativity. We briefly discuss the thermodynamics for the case c_{14}=0 where the horizon exists.
Highlights
The Lorentz invariance is an exact symmetry of special relativity, quantum field theories and the standard model of particle physics, and a local symmetry in freely falling inertial frames in general relativity [1]
In 1965, Roger Penrose proved the first modern singularity theorem [31] for which he is recognized with a Nobel Prize in physics last year [32]
We have analyzed all the possible exterior vacuum solutions with spherical symmetry allowed by the EA theory with static aether
Summary
The Lorentz invariance is an exact symmetry of special relativity, quantum field theories and the standard model of particle physics, and a local symmetry in freely falling inertial frames in general relativity [1]. The Lorentz violation in matter interactions is highly constrained by several precision experiments, see [2] for the latest example, while similar studies in gravity are not as well explored With this motivation, Jacobson and collaborators introduced and analyzed a general class of vector-tensor theories called the EinsteinAether (EA) theory [3,4,5,6,7]. The Cosmic Censorship Conjecture (CCC), introduced by Penrose in 1969 [33], does not permit singularities void of an event horizon as the end state of gravitational collapse for generic regular initial data and for a suitable matter system. Naked singularities are of current interest because they have observational properties quite different from a black hole Theoretically these regions of extreme gravity might have some hints of quantum gravity.
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