preprints.org > physical sciences > acoustics > doi: 10.20944/preprints202107.0019.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 30 June 2021 / Approved: 1 July 2021 / Online: 1 July 2021 (11:23:17 CEST)

We study spherically symmetric spacetimes in Einstein-aether theory in three different coordinate systems, the isotropic, Painlev\`e-Gullstrand, and Schwarzschild coordinates, 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 bya 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 $c_{14} \not= 0$, 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.

Einstein-aether theory; Lorentz violation; spherical spacetimes; exact solutions; black holes