# Hairy BTZ black hole and its analogue model in graphene

## TL;DR

This paper presents an exact solution for a hairy BTZ black hole in (2+1) dimensions, analyzes its quasinormal modes, and proposes a graphene-based analogue model to simulate its gravity-like phenomena.

## Contribution

It provides a novel analytical solution for a hairy BTZ black hole and develops a graphene analogue model to simulate its properties and phenomena.

## Key findings

- Quasinormal modes are equally spaced for spinless black holes.
- Spinning black holes have unequally spaced Dirac-like quasinormal modes.
- The graphene model can simulate black hole thermodynamics and gravity phenomena.

## Abstract

We obtain a novel exact analytical solution to Einstein-Maxwell-scalar gravity with negative cosmological constant in (2+1)-dimensions. The scalar field is minimally coupled to gravity and electromagnetism by the metric ansatz. On the one hand, we first find analytical results for the real part of quasinormal mode spectrum of a rotating hairy Ba\~{n}ados-Teitelboim-Zanelli (BTZ) black hole by solving the associated Dirac equation through the pseudo-Hermitian quantum mechanical tools within the framework of discrete-basis-set method. We then show that, in the spinless case, these quasinormal modes (QNMs) have equally spaced with respect to the related azimuthal quantum number, while the spinning BTZ black hole with scalar hair has Dirac-like unequally spaced discrete one. Moreover, the analytical results for these QNMs found here are in excellent agreement with those found in the literature for hairless BTZ black holes. On the other hand, we also develop an analogue model for this hairy Banados-Teitelboim-Zanelli black hole in graphene, by mapping it onto the hyperbolic pseudosphere surface with negative curvature. The model not only offers to make some predictions for the gravity-like phenomena in a curved graphene sheet but also paves the way for reproducing black hole thermodynamics scenarios in two-dimensional topological insulators.