# Fermion Clouds Around $z=0$ Lifshitz Black Holes

## TL;DR

This paper investigates fermionic perturbations around $z=0$ Lifshitz black holes by solving the Dirac equation, computing fermionic quasinormal modes, and deriving the quantized entropy and area spectra.

## Contribution

It introduces a method to compute fermionic quasinormal modes in $z=0$ Lifshitz black holes and derives their quantized entropy and area spectra using Maggiore's method.

## Key findings

- Fermionic quasinormal modes are computed using boundary conditions and iteration methods.
- The entropy and area spectra of the black hole are found to be equally spaced.
- The approach provides insights into fermionic perturbations in Lifshitz black hole backgrounds.

## Abstract

The Dirac equation is solved in the $z=0$ Lifshitz black hole ($Z0$LBH) spacetime. The set of equations representing the Dirac equation in the Newman-Penrose (NP) formalism is decoupled into a radial set and an angular set. The separation constant is obtained with the aid of the spin weighted spheroidal harmonics. The radial set of equations, which is independent of mass, is reduced to Zerilli equations (ZEs)\ with their associated potentials. In the near horizon (NH) region, these equations solved in terms of the Bessel functions of the first and second kinds arising from the fermionic perturbation on the background geometry. For computing the BQNMs instead of the ordinary quasinormal modes (QNMs), we first impose the purely ingoing wave condition at the event horizon. And then, Dirichlet boundary condition (DBC) and Newmann boundary condition (NBC) are applied in order to get the resonance conditions. For solving the resonance conditions we follow an iteration method. Finally, Maggiore's method (MM) is employed to derive the entropy/area spectra of the $Z0$LBH which are shown to be equidistant.