NUT Solutions in Einstein-Maxwell-scalar-Gauss-Bonnet Gravity

TL;DR

This paper numerically explores NUT black hole solutions in a four-dimensional Einstein-Maxwell-scalar-Gauss-Bonnet theory, revealing how scalar charges depend on coupling constants and providing detailed parameter analysis.

Contribution

It introduces the first numerical solutions for NUT black holes in Einstein-Maxwell-scalar-Gauss-Bonnet gravity with non-minimal coupling, including scalar charge dependence.

Findings

Explicit numerical NUT black hole solutions found.

Scalar charge depends on non-minimal coupling constants.

Detailed parameter space analysis provided.

Abstract

In this article, we consider a class of four-dimensional Einstein-Maxwell theory which is coupled non-minimally to a scalar field and the Gauss-Bonnet invariant. We mainly use the numerical methods to find the solutions to the theory, with the NUT twist. We find explicitly the numerical solutions to all of the field equations. To find the appropriate consistent numerical solutions, we use the the perturbative expansion of the fields asymptotically, as well as near horizon. The solutions describe the NUTty black holes with the scalar charge which also depend explicitly on the values of the non-minimal coupling constants. We provide a detailed numerical analysis of the solutions in terms of all existing parameters of the theory.