Black Holes in Einstein-Aether Theory

TL;DR

This paper explores black hole solutions in Einstein-Aether theory, revealing a family of regular solutions that closely resemble Schwarzschild black holes outside the horizon but differ inside, with unique aether flow characteristics.

Contribution

It characterizes the full family of static, spherically symmetric black hole solutions in Einstein-Aether theory, including their regularity conditions and internal structure.

Findings

Most solutions are regular at the metric horizon.

Only a subset is regular at the spin-0 horizon.

Solutions closely resemble Schwarzschild outside the horizon.

Abstract

We study black hole solutions in general relativity coupled to a unit timelike vector field dubbed the "aether". To be causally isolated a black hole interior must trap matter fields as well as all aether and metric modes. The theory possesses spin-0, spin-1, and spin-2 modes whose speeds depend on four coupling coefficients. We find that the full three-parameter family of local spherically symmetric static solutions is always regular at a metric horizon, but only a two-parameter subset is regular at a spin-0 horizon. Asymptotic flatness imposes another condition, leaving a one-parameter family of regular black holes. These solutions are compared to the Schwarzschild solution using numerical integration for a special class of coupling coefficients. They are very close to Schwarzschild outside the horizon for a wide range of couplings, and have a spacelike singularity inside, but differ inside quantitatively. Some quantities constructed from the metric and aether oscillate in the interior as the singularity is approached. The aether is at rest at spatial infinity and flows into the black hole, but differs significantly from the the 4-velocity of freely-falling geodesics.