Stability Analysis and Area Spectrum of 3-Dimensional Lifshitz Black Holes

TL;DR

This paper investigates the stability of a three-dimensional Lifshitz black hole under scalar and spinorial perturbations, providing analytical and numerical results that confirm stability and reveal an equally spaced area spectrum.

Contribution

It offers the first analytical expression for quasinormal frequencies of scalar fields in this context and confirms stability through numerical analysis of spinorial perturbations.

Findings

The black hole is stable under scalar and spinor perturbations.

Analytical quasinormal frequencies match numerical results.

The area spectrum of the black hole is equally spaced.

Abstract

In this work, we probe the stability of a $z=3$ three-dimensional Lifshitz black hole by using scalar and spinorial perturbations. We found an analytical expression for the quasinormal frequencies of the scalar probe field, which perfectly agree with the behavior of the quasinormal modes obtained numerically. The results for the numerical analysis of the spinorial perturbations reinforce the conclusion of the scalar analysis, i.e., the model is stable under scalar and spinor perturbations. As an application we found the area spectrum of the Lifshitz black hole, which turns out to be equally spaced.