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

References in corpus (11)

• Black holes in Einstein-aether and Horava-Lifshitz gravity
• Numerical simulations of gravitational collapse in Einstein-aether theory
• Perturbations and quasi-normal modes of black holes in Einstein-Aether theory
• Towards thermodynamics of universal horizons in Einstein-æther theory
• Generic features of Einstein-Aether black holes
• Circular orbits in Kerr-Taub-NUT spacetime and their implications for accreting black holes and naked singularities
• Quasinormal ringing of black holes in Einstein aether theory
• New look at black holes: Existence of universal horizons
• Three-dimensional charged Einstein-aether black holes and Smarr formula
• Gravitational quasinormal modes of black holes in Einstein-aether theory
• Entropies and The First Laws of Black Hole Thermodynamics in Einstein-aether-Maxwell Theory

Cited by in corpus (9)

• Optical appearance of Einstein-Æther black hole surrounded by thin disk
• Odd-parity stability of black holes in Einstein-Aether gravity
• Thermodynamics of Einstein-Aether Black Holes
• Integrability and Cosmological Solutions in Einstein-aether-Weyl theory
• Is Birkhoff's Theorem Valid in Einstein-Aether Theory?
• Revisiting linear stability of black hole odd-parity perturbations in Einstein-Aether gravity
• Black Hole Solutions in Non-Minimally Coupled Weyl Connection Gravity
• Cylindrical Gravitational Waves in Einstein-Aether Theory
• Complete Classification of Analytical Models in Einstein-Aether Cosmology