A new model of regular black hole in $(2+1)$ dimensions

TL;DR

This paper introduces a novel regular black hole model in (2+1) dimensions incorporating matter fields, modifies the first law of thermodynamics accordingly, and demonstrates the formalism's effectiveness in calculating black hole energy.

Contribution

The paper presents a new regular black hole solution in (2+1) dimensions with matter fields and develops a modified first law of thermodynamics for such black holes.

Findings

New regular black hole solution with matter fields in (2+1) dimensions.

A consistent thermodynamic framework with a local energy variation.

Effective method to compute total energy of regular black holes.

Abstract

We provide a new regular black hole solution in $(2+1)$ dimensions with presence of matter fields in the energy momentum tensor, having its core a flat or (A)dS structure. Since the first law of thermodynamics for regular black holes is modified by the presence of the matter fields, we provide a new version of the first law, where a local definition of the variation of energy is defined, and, where the entropy and temperature are consistent with the previously known in literature. It is shown that the signs of the variations of the local definition of energy and of the total energy coincide. Furthermore, at infinite, the usual first law $dM=TdS$ is recovered. It is showed that the formalism used is effective to compute the total energy of regular black holes in $(2+1)$ with presence of matter in the energy momentum tensor. This latter suggests the potential applicability of this formalism to calculate the mass of other models of regular black holes in $d \ge 4$ dimensions.