Global Structure of Black Holes in String Theory with Gauss-Bonnet Correction in Various Dimensions

TL;DR

This paper investigates the global structures of black holes in Einstein-Gauss-Bonnet-dilaton gravity across various dimensions, revealing milder non-central singularities and different global types, including Schwarzschild and AdS black holes.

Contribution

It provides a detailed analysis of black hole singularities and global structures in Einstein-Gauss-Bonnet-dilaton gravity, highlighting the existence of milder non-central singularities and diverse global configurations.

Findings

Non-central singularities are milder than Schwarzschild solutions.

Black holes exhibit three global structure types: Schwarzschild, Schwarzschild-AdS, and regular AdS.

Singularities at the center can be stronger or milder depending on parameters.

Abstract

We study global structures of black hole solutions in Einstein gravity with Gauss-Bonnet term coupled to dilaton in various dimensions. In particular we focus on the problem whether the singularity is weakened due to the Gauss-Bonnet term and dilaton. We find that there appears the non-central singularity between horizon and the center in many cases, where the metric does not diverge but the Kretschmann invariant does diverge. Hence this is a singularity, but we find the singularity is much milder than the Schwarzschild solution and the non-dilatonic one. We discuss the origin of this "fat" singularity. In other cases, we encounter singularity at the center which is much stronger than the usual one. We find that our black hole solutions have three different types of the global structures; the Schwarzschild, Schwarzschild-AdS and "regular AdS black hole" types.