Lower dimensional black holes in nonlinear electrodynamics: causal structure and scalar perturbations

TL;DR

This paper explores the causal structure and scalar perturbations of charged black holes in a 2+1 nonlinear electrodynamics theory, revealing a rich classification and demonstrating stability under linear scalar perturbations.

Contribution

It provides a comprehensive classification of black hole solutions in nonlinear electrodynamics and analyzes their stability and quasinormal modes.

Findings

Identified three distinct groups of black hole solutions based on singularity and horizon behavior.

All analyzed geometries are stable under scalar linear perturbations.

Calculated quasinormal spectra for different black hole cases.

Abstract

We study the charged black hole solutions of a 2+1 nonlinear electrodynamical theory with cosmological constant. Considered as a one-parameter group of theories (the exponent of the squared Maxwell tensor) the causal structure of all possible black holes is scrutinized. We analyze the singularity character that each theory delivers together with their horizons and the plausible limitations in the black hole charges. The investigation demonstrates a rich structure of three different groups of theories, according to the qualitative behavior of the singularity, horizons and limitations in the geometric charges. For such groups we study the effect of a scalar field propagating in the fixed black holes spacetime. All geometries analyzed were stable to such linear perturbations, these evolving as usual quasinormal spectra of the black holes that we calculate in different cases.