Regular Multi-Horizon Black Holes in Modified Gravity with Non-Linear Electrodynamics

TL;DR

This paper explores regular multi-horizon black holes in various modified gravity theories coupled with non-linear electrodynamics, analyzing their thermodynamics and revealing unique properties such as temperature behavior and entropy characteristics.

Contribution

It provides explicit examples of regular multi-horizon black hole solutions in Einstein, $F(R)$, and Gauss-Bonnet gravity coupled with non-linear electrodynamics, along with their thermodynamic analysis.

Findings

Temperature vanishes at extremal limit, with larger horizons having higher temperature.

Specific heat becomes positive at high temperatures, unlike standard black holes.

Entropy can become negative in Gauss-Bonnet gravity.

Abstract

We investigated the regular multi-horizon black holes in the Einstein gravity, $F(R)$ gravity and the 5 dimensional Gauss-Bonnet gravity, all of them coupled with non-linear electrodynamics. We presented several explicit examples of the actions which admit the solutions describing regular black hole space-time with multi-horizons. Thermodynamics of the obtained black hole solutions is studied. The explicit expressions of the temperature, the entropy, the thermodynamical energy and the free energy are obtained. Although the temperature vanishes in the extremal limit where the radii of the two horizons coincide with each other as in the standard multi-horizon black hole like the Reissner-Nordstr\" om black hole or the Kerr black hole, the larger temperature corresponds to the larger horizon radius. This is different from the standard black holes, where the larger temperature corresponds to the smaller horizon radius. We also found that the specific heat becomes positive for the large temperature, which is also different from the standard black holes, where the specific heat is negative. It should be also noted that the thermodynamical energy is not identical with the ADM mass. Furthermore in case of the Gauss-Bonnet gravity, it is demonstrated that the entropy can become negative.