Black Holes in the Dilatonic Einstein-Gauss-Bonnet Theory in Various Dimensions III -- Asymptotically AdS Black Holes with $k=\pm 1$ --

TL;DR

This paper investigates black hole solutions in dilatonic Einstein-Gauss-Bonnet gravity with negative cosmological constant across various dimensions, finding exact and numerical solutions with different horizon geometries and analyzing their properties relevant to AdS/CFT correspondence.

Contribution

It provides new exact and numerical asymptotically AdS black hole solutions in higher-dimensional dilatonic Einstein-Gauss-Bonnet gravity with detailed horizon structure analysis.

Findings

Exact AdS solution for k=1

Massless black hole solution for k=-1

Numerical solutions in D=4--6 and D=10 dimensions

Abstract

We study black hole solutions in the Einstein-Gauss-Bonnet gravity with the dilaton and a negative ``cosmological constant''. We derive the field equations for the static spherically symmetric ($k=1$) and hyperbolically symmetric ($k=-1$) spacetime in general $D$ dimensions. The system has some scaling symmetries which are used in our analysis of the solutions. We find exact solutions, i.e., regular AdS solution for $k=1$ and a massless black hole solution for $k=-1$. Nontrivial asymptotically AdS solutions are obtained numerically in D=4 -- 6 and 10 dimensional spacetimes. For spherically symmetric solutions, there is the minimum horizon radius below which no solution exists in D=4 -- 6. However in D=10, there is not such lower bound but the solution continues to exist to zero horizon size. For hyperbolically symmetric solution, there is the minimum horizon radius in all dimensions. Our solution can be used for investigations of the boundary theory through AdS/CFT correspondence.