Regular black holes in Einstein cubic gravity

Abstract

We investigate the effects of the Einstein cubic gravity (ECG) on regular black hole solutions driven by nonlinear electrodynamics (NLE) sources. The ECG tends to form a naked singularity at the origin for a high ECG coupling constant. Assuming that ECG provides only perturbative corrections to the regular magnetic charged solutions, we found modified regular solutions with a de Sitter-like core whose cosmological constant depends on the magnetic charge and the ECG coupling constant. The thermodynamic stability is investigated by means of the Hawking temperature and the heat capacity. In fact, for a small charge and ECG coupling, the Hawking temperature is regularized, leaving a thermodynamic stable remnant for a small $r_h \neq 0$. The heat capacity reveals that the ECG regular black hole undergoes a phase transition between an unstable into a stable configuration.