Black Holes in the Dilatonic Einstein-Gauss-Bonnet Theory in Various Dimensions IV - Topological Black Holes with and without Cosmological Term

TL;DR

This paper investigates topological black hole solutions in Einstein-Gauss-Bonnet-dilaton gravity with a positive cosmological constant across various dimensions, revealing bounds on black hole sizes and asymptotic behaviors.

Contribution

It provides the first numerical construction of hyperbolic topological black holes with positive cosmological constant in higher dimensions and analyzes their properties.

Findings

Black holes exist only for certain horizon sizes.

Spacetime approaches anti-de Sitter asymptotically.

No solutions likely without cosmological constant for hyperbolic space.

Abstract

We study black hole solutions in the Einstein gravity with Gauss-Bonnet term, the dilaton and a positive "cosmological constant" in various dimensions. Physically meaningful black holes with a positive cosmological term are obtained only for those in static spacetime with $(D-2)$-dimensional hyperbolic space of negative curvature and $D>4$. We construct such black hole solutions of various masses numerically in $D=5,6$ and 10 dimensional spacetime and discuss their properties. In spite of the positive cosmological constant the spacetime approach anti-de Sitter spacetime asymptotically. The black hole solutions exist for a certain range of the horizon radius, i.e., there are lower and upper bounds for the size of black holes. We also argue that it is quite plausible that there is no black hole solution for hyperbolic space in the case of no cosmological constant.