Extremal black holes in D=4 Gauss-Bonnet gravity

TL;DR

This paper demonstrates the existence of asymptotically flat extremal black holes with degenerate horizons in four-dimensional Einstein-Maxwell-Dilaton-Gauss-Bonnet gravity, revealing new solutions with specific charge and coupling properties.

Contribution

It introduces novel extremal black hole solutions in 4D Gauss-Bonnet gravity with detailed analysis of their properties and critical dilaton coupling values.

Findings

Black holes exist for dilaton coupling 0 ≤ a² < a²_cr.

Purely electric solutions are numerically constructed.

Entropy of extremal black holes is twice the Bekenstein-Hawking entropy.

Abstract

We show that four-dimensional Einstein-Maxwell-Dilaton-Gauss-Bonnet gravity admits asymptotically flat black hole solutions with a degenerate event horizon of the Reissner-Nordstr\"om type $AdS_2\times S^2$. Such black holes exist for the dilaton coupling constant within the interval $0\leq a^2<a^2_{\rm cr}$. Black holes must be endowed with an electric charge and (possibly) with magnetic charge (dyons) but they can not be purely magnetic. Purely electric solutions are constructed numerically and the critical dilaton coupling is determined $a_{\rm cr}\simeq 0.488219703$. For each value of the dilaton coupling $a$ within this interval and for a fixed value of the Gauss--Bonnet coupling $\alpha$ we have a family of black holes parameterized by their electric charge. Relation between the mass, the electric charge and the dilaton charge at both ends of the allowed interval of $a$ is reminiscent of the BPS condition for dilaton black holes in the Einstein-Maxwell-Dilaton theory. The entropy of the DGB extremal black holes is twice the Bekenstein-Hawking entropy.