Phases of 4D Scalar-tensor black holes coupled to Born-Infeld nonlinear electrodynamics

TL;DR

This paper explores new charged black hole solutions in scalar-tensor theories with nonlinear electrodynamics, revealing multiple phases, their causal structures, and potential phase transitions, thus extending understanding beyond classical no-hair theorems.

Contribution

It introduces novel numerical solutions for charged black holes in scalar-tensor theories coupled with Born-Infeld electrodynamics, including phases with non-trivial scalar fields.

Findings

Existence of multiple black hole phases with different scalar field configurations.

Black holes have a single, non-degenerate horizon similar to Schwarzschild.

Thermodynamic analysis suggests possible phase transitions.

Abstract

Recent results show that when non-linear electrodynamics is considered the no-scalar-hair theorems in the scalar-tensor theories (STT) of gravity, which are valid for the cases of neutral black holes and charged black holes in the Maxwell electrodynamics, can be circumvented. What is even more, in the present work, we find new non-unique, numerical solutions describing charged black holes coupled to non-linear electrodynamics in a special class of scalar-tensor theories. One of the phases has a trivial scalar field and coincides with the corresponding solution in General Relativity. The other four phases that we find are characterized by the value of the scalar field charge. The causal structure and some aspects of the stability of the solutions have also been studied. For the scalar-tensor theories considered, the black holes have a single, non-degenerate horizon, i.e., their causal structure resembles that of the Schwarzschild black hole. The thermodynamic analysis of the stability of the solutions indicates that a phase transition may occur.