Quasinormal modes of BTZ black hole and Hawking-like radiation in graphene

TL;DR

This paper develops an analytical method to study quasinormal modes of BTZ black holes within a graphene model, predicting observable Hawking-like radiation effects in curved graphene sheets.

Contribution

It introduces a novel analytical algorithm for Dirac Hamiltonian solutions in BTZ black hole fields using pseudo-Hermitian formalism, applicable to both spinning and non-spinning cases.

Findings

Reproduces exact quasinormal mode frequencies for non-spinning BTZ black holes.

Provides analytical predictions for spinning BTZ black hole quasinormal modes.

Suggests potential experimental detection of Hawking-like radiation in curved graphene.

Abstract

The Ba\~{n}ados-Teitelboim-Zanelli (BTZ) black hole model corresponds to a solution of (2+1)-dimensional Einstein gravity with negative cosmological constant, and by a conformal rescaling its metric can be mapped onto the hyperbolic pseudosphere surface (Beltrami trumpet) with negative curvature. Beltrami trumpet shaped graphene sheets have been predicted to emit Hawking radiation that is experimentally detectable by a scanning tunnelling microscope. Here, for the first time we present an analytical algorithm that allows variational solutions to the Dirac Hamiltonian of graphene pseudoparticles in BTZ black hole gravitational field by using an approach based on the formalism of pseudo-Hermitian Hamiltonians within a discrete-basis-set method. We show that our model not only reproduces the exact results for the real part of quasinormal mode frequencies of (2+1)-dimensional spinless BTZ black hole, but also provides analytical results for the real part of quasinormal modes of spinning BTZ black hole, and also offers some predictions for the observable effects with a view to gravity-like phenomena in a curved graphene sheet.