New rotating black holes in non-linear Maxwell $f({\cal R})$ gravity

TL;DR

This paper finds new rotating black hole solutions in a modified gravity theory with non-linear electromagnetic fields, analyzing their properties and stability, revealing novel thermodynamic behaviors including negative temperatures.

Contribution

It provides analytical solutions for rotating black holes in $f({\cal R})$ gravity with non-linear electrodynamics, including thermodynamic analysis and stability conditions.

Findings

Existence of two solution branches, one general relativity limit and one purely from modified gravity.

Discovery of thermodynamically stable black holes with negative temperatures.

Identification of conditions for horizon formation and naked singularities.

Abstract

We investigate static and rotating charged spherically symmetric solutions in the framework of $f({\cal R})$ gravity, allowing additionally the electromagnetic sector to depart from linearity. Applying a convenient, dual description for the electromagnetic Lagrangian, and using as an example the square-root $f({\cal R})$ correction, we solve analytically the involved field equations. The obtained solutions belong to two branches, one that contains the Kerr-Newman solution of general relativity as a particular limit and one that arises purely from the gravitational modification. The novel black hole solution has a true central singularity which is hidden behind a horizon, however for particular parameter regions it becomes a naked one. Furthermore, we investigate the thermodynamical properties of the solutions, such as the temperature, energy, entropy, heat capacity and Gibbs free energy. We extract the entropy and quasilocal energy positivity conditions, we show that negative-temperature, ultracold, black holes are possible, and we show that the obtained solutions are thermodynamically stable for suitable model parameter regions.