Spectroscopy of $z=0$ Lifshitz Black Hole

TL;DR

This paper investigates the thermodynamic properties and spectral characteristics of a specific Lifshitz black hole with zero dynamical exponent, revealing evenly spaced entropy and area spectra through quasinormal mode analysis.

Contribution

It provides the first detailed analysis of the thermodynamics and spectroscopy of the $z=0$ Lifshitz black hole, including quasinormal modes and quantized spectra.

Findings

Entropy and area spectra are equally spaced.

Quasinormal modes are computed from the near-horizon Zerilli equation.

The quasilocal mass is derived using Wald's entropy and Hawking temperature.

Abstract

We studied the thermodynamics and spectroscopy of a $4$-dimensional, $z=0$ Lifshitz black hole ($Z0$LBH). Using the Wald's entropy formula and the Hawking temperature, we derived the quasilocal mass of the $Z0$LBH. Based on the exact solution to the near-horizon Zerilli equation of the massive scalar waves, we computed the quasinormal modes of the $Z0$LBH via employing the adiabatic invariant quantity for the $Z0$LBH. This study shows that the entropy and area spectra of the $Z0$LBH are equally spaced.