The Attractor Mechanism in Gauss-Bonnet Gravity

TL;DR

This paper investigates the attractor mechanism in extremal black holes within five-dimensional Gauss-Bonnet gravity, demonstrating its persistence under certain conditions and its breakdown in non-extremal cases through analytical and numerical methods.

Contribution

It extends the attractor mechanism concept to Gauss-Bonnet gravity, providing analytical evidence and numerical examples of its validity and failure.

Findings

Attractor mechanism holds in extremal Gauss-Bonnet black holes under specific conditions.

Numerical solutions confirm the attractor behavior for a simple scalar model.

The mechanism fails in non-extremal black hole solutions.

Abstract

We study extremal black hole solutions of D=5 Gauss-Bonnet gravity coupled to a system of gauge and scalar fields. As in Einstein gravity, we find that the values of the scalar fields on the horizon must extremize a certain effective potential that depends on the black hole charges. If the matrix of second derivatives of the effective potential at this extremum has positive eigenvalues, we give evidence, based on a near horizon perturbative expansion, that the attractor mechanism continues to hold in this general class of theories. We numerically construct solutions to a particular simple single scalar field model that display the attractor mechanism over a wide range of asymptotic values for the scalar field. We also numerically construct non-extremal solutions and show that the attractor mechanism fails to hold away from extremality.