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

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.

25 pages, 16 figures

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• Black Holes in Higher Dimensional Gravity Theory with Quadratic in Curvature Corrections
• Global Structure of Black Holes in String Theory with Gauss-Bonnet Correction in Various Dimensions
• Fubini instantons in Dilatonic Einstein-Gauss-Bonnet theory of gravitation
• Black-Hole Solutions to Einstein's Equations in the Presence of Matter and Modifications of Gravitation in Extra Dimensions