Spherical Solutions in Einstein-Aether Theory: Static Aether and Stars

TL;DR

This paper explores static, spherically symmetric solutions in Einstein-Aether theory, revealing a family of solutions with a minimal area sphere and singularities, and demonstrates the existence and stability of perfect fluid star solutions with these exteriors.

Contribution

It provides analytical static aether solutions in Einstein-Aether theory, characterizes their properties, and shows the existence and stability of perfect fluid stars with these exteriors.

Findings

Existence of a three-parameter family of solutions

Imposition of asymptotic flatness reduces parameters to one (mass)

Regular star solutions with static aether exteriors are found and their stability range identified

Abstract

The time independent spherically symmetric solutions of General Relativity (GR) coupled to a dynamical unit timelike vector are studied. We find there is a three-parameter family of solutions with this symmetry. Imposing asymptotic flatness restricts to two parameters, and requiring that the aether be aligned with the timelike Killing field further restricts to one parameter, the total mass. These "static aether" solutions are given analytically up to solution of a transcendental equation. The positive mass solutions have spatial geometry with a minimal area 2-sphere, inside of which the area diverges at a curvature singularity occurring at an extremal Killing horizon that lies at a finite affine parameter along a radial null geodesic. Regular perfect fluid star solutions are shown to exist with static aether exteriors, and the range of stability for constant density stars is identified.