Scalar-tensor black holes coupled to Euler-Heisenberg nonlinear electrodynamics

TL;DR

This paper numerically constructs charged black hole solutions in scalar-tensor theories coupled with Euler-Heisenberg nonlinear electrodynamics, revealing simpler causal structures compared to General Relativity due to scalar field effects.

Contribution

It provides the first numerical solutions for charged black holes in scalar-tensor theories with nonlinear electrodynamics, extending no-hair theorems to these cases.

Findings

Black holes have a single, non-degenerate horizon.

Scalar field presence simplifies the causal structure.

Solutions differ from GR counterparts in causal properties.

Abstract

The no-scalar-hair conjecture rules out the existence of asymptotically flat black holes with a scalar dressing for a large class of theories. No-scalar-hair theorems have been proved for the cases of neutral black holes and for charged black holes in the Maxwell electrodynamics. These theorems, however, do not apply in the case of non-linear electrodynamics. In the present work numerical solutions describing charged black holes coupled to Euler-Heisenberg type non-linear electrodynamics in scalar-tensor theories of gravity with massless scalar field are found. In comparison to the corresponding solution in General Relativity the presented solution has a simpler causal structure the reason for which is the presence of the scalar field. The present class of black holes has a single, non-degenerate horizon, i.e., its causal structure resembles that of the Schwarzschild black hole.