Even- and odd-parity stabilities of black holes in Einstein-Aether gravity

TL;DR

This paper investigates the linear stability of static, spherically symmetric black holes in Einstein-Aether gravity against both even- and odd-parity perturbations, revealing the propagation characteristics and stability conditions of various perturbation modes.

Contribution

It formulates a gauge-invariant perturbation theory in the Aether-orthogonal frame and analyzes the stability and propagation speeds of perturbations, extending stability analysis to black hole backgrounds in Einstein-Aether gravity.

Findings

Three dynamical degrees of freedom in the even-parity sector.

Propagation speeds match those of Minkowski background perturbations.

No additional small-scale stability conditions are found for black holes.

Abstract

In Einstein-Aether theories with a timelike unit vector field, we study the linear stability of static and spherically symmetric black holes against both even- and odd-parity perturbations. For this purpose, we formulate a gauge-invariant black hole perturbation theory in the background Aether-orthogonal frame where the spacelike property of hypersurfaces orthogonal to the timelike Aether field is always maintained even inside the metric horizon. Using a short-wavelength approximation with large radial and angular momenta, we show that, in general, there are three dynamical degrees of freedom arising from the even-parity sector besides two propagating degrees of freedom present in the odd-parity sector. The propagation speeds of even-parity perturbations and their no-ghost conditions coincide with those of tensor, vector, and scalar perturbations on the Minkowski background, while the odd sector contains tensor and vector modes with the same propagation speeds as those in the even-parity sector (and hence as those on the Minkowski background). Thus, the consistent study of black hole perturbations in the Aether-orthogonal frame on static and spherically symmetric backgrounds does not add new small-scale stability conditions to those known for the Minkowski background in the literature.