Asymptotic charged BTZ black hole solutions

TL;DR

This paper derives new asymptotic charged BTZ black hole solutions within Einstein-nonlinear electromagnetic theory, analyzes their thermodynamics, and demonstrates their stability across the entire phase space.

Contribution

It introduces three novel black hole solutions with nonlinear electromagnetic fields and confirms their thermodynamic consistency and stability.

Findings

Solutions have the same asymptotic behavior as charged BTZ black holes.

Thermodynamic quantities satisfy the first law of thermodynamics.

Black holes are stable in the entire phase space.

Abstract

The well-known $(2+1)$-dimensional Reissner-Nordstrom (BTZ) black hole can be generalized to three dimensional Einstein-nonlinear electromagnetic field, motivated from obtaining a finite value for the self-energy of a pointlike charge. Considering three types of nonlinear electromagnetic fields coupled with Einstein gravity, we derive three kinds of black hole solutions which their asymptotic properties are the same as charged BTZ solution. In addition, we calculate conserved and thermodynamic quantities of the solutions and show that they satisfy the first law of thermodynamics. Finally, we perform a stability analysis in the canonical ensemble and show that the black holes are stable in the whole phase space.