Scalar field perturbations in asymptotically Lifshitz black holes

TL;DR

This paper investigates the stability of asymptotically Lifshitz black holes under scalar perturbations, computes quasinormal modes for specific cases, and demonstrates stability under certain boundary conditions.

Contribution

It provides the first explicit calculation of quasinormal modes for Lifshitz black holes with z=2 and analyzes stability for various dynamical exponents.

Findings

Lifshitz black holes are stable under scalar perturbations with suitable boundary conditions.

Quasinormal modes for z=2 are purely imaginary, indicating damping.

Includes analysis of the z=3 black hole in three-dimensional massive gravity.

Abstract

We consider scalar field perturbations about asymptotically Lifshitz black holes with dynamical exponent z in D dimensions. We show that, for suitable boundary conditions, these Lifshitz black holes are stable under scalar field perturbations. For z=2, we explicitly compute the quasinormal mode frecuencies, which result to be purely imaginary, and then obtain the damping-off of the scalar field perturbation in these backgrounds. The general analysis includes, in particular, the z=3 black hole solution of three-dimensional massive gravity.