A novel exact magnetic black hole solution in four-dimensional extended scalar-tensor-Gauss-Bonnet theory

TL;DR

This paper presents the first exact asymptotically flat static spherically symmetric black hole solution in four-dimensional extended scalar-tensor-Gauss-Bonnet theory, incorporating nonlinear electrodynamics with magnetic charge and scalar hair.

Contribution

It introduces a novel exact black hole solution in ESTGB theory with nonlinear electrodynamics, featuring scalar hair dependent on magnetic charge, expanding the understanding of black hole configurations in modified gravity.

Findings

Solution is asymptotically flat, static, spherically symmetric.

Describes black holes with different structures based on parameters.

Includes cases similar to Schwarzschild and Reissner-Nordström black holes.

Abstract

In this work the first exact asymptotically flat static and spherically symmetric black hole solution for $(3+1)$-dimensional ESTGB is presented, with a model of nonlinear electrodynamics -- that reduces to Maxwell's theory in the weak field limit and satisfies the weak energy condition -- as a source. The solution has a nonzero magnetic charge, and scalar hair, which turns out to be dependent of the magnetic charge. It is characterized by the ADM mass $m$ and the magnetic charge $q$. Depending on the range of these parameters, the solution describes black holes with different structure. In the case $m\geq0$ and $q\geq0$, it shares many of the characteristics of the Schwarzschild solution. For $m>0$ and $q<0$, it is akin to the Reissner-Nordstr\"om metric. In the case $m=0$, it represents a purely magnetic black hole.