Odd-parity stability of black holes in Einstein-Aether gravity

TL;DR

This paper investigates the stability of black holes in Einstein-Aether gravity against odd-parity perturbations, deriving conditions to avoid instabilities and applying them to known solutions, revealing stability constraints.

Contribution

It provides the first detailed stability analysis of black holes in Einstein-Aether theory for odd-parity modes, identifying conditions for avoiding ghosts and Laplacian instabilities.

Findings

Some black hole solutions are unstable and can be excluded.

The Schwarzschild solution with specific parameters is prone to angular instabilities.

Certain parameter choices lead to stable black hole solutions against odd-parity perturbations.

Abstract

In Einstein-Aether theory, we study the stability of black holes against odd-parity perturbations on a spherically symmetric and static background. For odd-parity modes, there are two dynamical degrees of freedom arising from the tensor gravitational sector and Aether vector field. We derive general conditions under which neither ghosts nor Laplacian instabilities are present for these dynamical fields. We apply these results to concrete black hole solutions known in the literature and show that some of those solutions can be excluded by the violation of stability conditions. The exact Schwarzschild solution present for $c_{13} = c_{14} = 0$, where $c_i$'s are the four coupling constants of the theory with $c_{ij}=c_i + c_j$, is prone to Laplacian instabilities along the angular direction throughout the horizon exterior. However, we find that the odd-parity instability of high radial and angular momentum modes is absent for black hole solutions with $c_{13} = c_4 = 0$ and $c_1 \geq 0$.