Spherically symmetric exact vacuum solutions in Einstein-aether theory

TL;DR

This paper derives exact spherically symmetric vacuum solutions in Einstein-aether theory across different coordinate systems, revealing a class of solutions that include black hole-like structures with unique singularity properties.

Contribution

It presents new exact static and dynamic solutions in Einstein-aether theory, including a parameter-dependent class that generalizes Schwarzschild black holes and exhibits novel horizon and singularity features.

Findings

Existence of a parameter-dependent class of static solutions

Solutions reduce to Schwarzschild black holes when the parameter is zero

Presence of a marginally trapped throat with distinct spacetime regions

Abstract

We study spherically symmetric spacetimes in Einstein-aether theory in three different coordinate systems, the isotropic, Painlev\`e-Gullstrand, and Schwarzschild coordinates, in which the aether is always comoving, 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 by a 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.