Spherically Symmetric Exact Vacuum Solutions in Einstein-Aether Theory

We study spherically symmetric spacetimes in Einstein-aether theory three different coordinate systems, the isotropic, Painlevè-Gullstrand, and Schwarzschild coordinates, which aether is always comoving, present both time-dependent time-independent exact vacuum solutions. In particular, isotropic coordinates we find a class of static solutions characterized by single parameter c14 closed forms, satisfies all current observational constraints theory, reduces to black hole solution decoupling limit (c14=0). However, as long c14≠0, marginally trapped throat with finite non-zero radius exists, on one side it spacetime asymptotically flat, while other becomes singular within proper distance from throat, although geometric area infinitely large at singularity. Moreover, singularity strong curvature singularity, Ricci Kretschmann scalars become large.