# Fermionic field perturbations of a three-dimensional Lifshitz black hole in conformal gravity

## TL;DR

This paper investigates the behavior of massless fermionic fields around a three-dimensional Lifshitz black hole in conformal gravity, analyzing stability, spectra, and absorption properties through analytical methods.

## Contribution

It provides the first analytical computation of quasinormal modes, area spectrum, and absorption cross section for fermionic fields in this specific Lifshitz black hole background.

## Key findings

- Fermionic perturbations are stable in this background.
- Area and entropy spectra are evenly spaced.
- Absorption cross section varies with frequency and angular momentum.

## Abstract

We study the propagation of massless fermionic fields in the background of a three-dimensional Lifshitz black hole, which is a solution of conformal gravity. The black hole solution is characterized by a null dynamical exponent. Then, we compute analytically the quasinormal modes, the area spectrum, and the absorption cross section for fermionic fields. The analysis of the quasinormal modes shows that the fermionic perturbations are stable in this background. The area and entropy spectrum are evenly spaced. At the low frequency limit, it is observed that there is a range of values of the angular momentum of the mode that contributes to the absorption cross section, whereas it vanishes at the high frequency limit. In addition, by a suitable change of variables a gravitational soliton can also be obtained and the stability of the quasinormal modes are studied and ensured.