Black Holes in the Scalar-Tensor Formulation of 4D Einstein-Gauss-Bonnet Gravity: Uniqueness of Solutions, and a New Candidate for Dark Matter

TL;DR

This paper investigates static black holes in a 4D Einstein-Gauss-Bonnet gravity theory, establishing their uniqueness, thermodynamic properties, and proposing black hole remnants as dark matter candidates.

Contribution

It demonstrates the uniqueness of static, spherically-symmetric black hole solutions in the theory and explores their potential role as dark matter.

Findings

Unique static, spherically-symmetric black hole solution identified.

No asymptotically-flat, time-dependent perturbations allowed.

Black hole remnants could serve as dark matter candidates.

Abstract

In this work we study static black holes in the regularized 4D Einstein-Gauss-Bonnet theory of gravity; a shift-symmetric scalar-tensor theory that belongs to the Horndeski class. This theory features a simple black hole solution that can be written in closed form, and which we show is the unique static, spherically-symmetric and asymptotically-flat black hole vacuum solution of the theory. We further show that no asymptotically-flat, time-dependent, spherically-symmetric perturbations to this geometry are allowed, which suggests that it may be the only spherically-symmetric vacuum solution that this theory admits (a result analogous to Birkhoff's theorem). Finally, we consider the thermodynamic properties of these black holes, and find that their final state after evaporation is a remnant with a size determined by the coupling constant of the theory. We speculate that remnants of this kind from primordial black holes could act as dark matter, and we constrain the parameter space for their formation mass, as well as the coupling constant of the theory.