Scalar Perturbations of two-dimensional Horava-Lifshitz Black Holes

TL;DR

This paper investigates the stability of two-dimensional Horava-Lifshitz black holes by analyzing scalar field perturbations and quasinormal modes, revealing damping behavior and potential instability for large scalar masses.

Contribution

It provides the first analysis of scalar perturbations and quasinormal modes for 2D Horava-Lifshitz black holes, highlighting stability characteristics and instability conditions.

Findings

Quasinormal modes are discrete and purely imaginary.

Perturbations exhibit damping behavior.

Large scalar masses may lead to instability.

Abstract

In this article, we study the stability of black hole solutions found in the context of dilatonic Horava-Lifshitz gravity in $1+1$ dimensions by means of the quasinormal modes approach. In order to find the corresponding quasinormal modes, we consider the perturbations of massive and massless scalar fields minimally coupled to gravity. In both cases, we found that the quasinormal modes have a discrete spectrum and are completely imaginary, which leads to damping modes. For a massive scalar field and a non-vanishing cosmological constant, our results suggest unstable behaviour for large values of the scalar field mass.