Rotating black holes in general relativity coupled to nonlinear electrodynamics

TL;DR

This paper derives exact solutions for magnetically charged black holes in general relativity coupled with nonlinear electrodynamics, constructs rotating versions using the Newman-Janis algorithm, and analyzes their thermodynamic and conserved properties.

Contribution

It introduces a new exact magnetically charged black hole solution in GR with NED and extends it to rotating black holes with detailed thermodynamic analysis.

Findings

Deviations in thermodynamic quantities from Kerr black holes due to NED.

Exact expressions for mass, temperature, entropy, and free energy.

Conservation laws and relations like K_{\chi}=2S_+T_+" for the rotating black holes.

Abstract

We find an exact spherically symmetric magnetically charged black hole solution to general relativity (GR) coupled to nonlinear electrodynamics (NED) with an appropriate Lagrangian density. In turn, starting with this spherical black hole as a seed metric, we construct a rotating spacetime, a modification of Kerr black hole, using the revised Newman-Janis algorithm that depends on mass, spin, and a NED parameter $g$. We find an exact expression for thermodynamic quantities of the black holes like the mass, Hawking temperature, entropy, heat capacity, and free energy expressed in terms of horizon radius, and they show significant deviations from the Kerr case owing to NED. We also calculate analytical expressions for effective Komar mass and angular momentum for the rotating black hole and demonstrate that the Komar conserved quantity corresponding to the null Killing vector at horizon obeys $\mathcal{K}_{\chi}=2S_+T_+.$ The radiating counterpart renders a generalization of Carmeli's spacetime as well as Vaidya's spacetime in the appropriate limits.