Spherically Symmetric Analytic Solutions and Naked Singularities in Einstein-Aether Theory

Abstract

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.

21 pages and 9 figures

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