Topological black holes in the dimensionally continued gravity

TL;DR

This paper explores topological black holes within Lovelock gravity, analyzing their thermodynamics, horizon curvatures, and comparing them to Einstein-Maxwell black holes in higher dimensions.

Contribution

It introduces a unified framework for topological black holes in Lovelock gravity with simplified parameters and examines their thermodynamic properties and differences based on horizon curvature.

Findings

Black holes with various horizon curvatures are characterized in Lovelock gravity.

Thermodynamic properties depend on the horizon's curvature type.

Comparison with Einstein-Maxwell black holes highlights unique features.

Abstract

We investigate the topological black holes in a special class of Lovelock gravity. In the odd dimensions, the action is the Chern-Simons form for the anti-de Sitter group. In the even dimensions, it is the Euler density constructed with the Lorentz part of the anti-de Sitter curvature tensor. The Lovelock coefficients are reduced to two independent parameters: cosmological constant and gravitational constant. The event horizons of these topological black holes may have constant positive, zero or negative curvature. Their thermodynamics is analyzed and electrically charged topological black holes are also considered. We emphasize the differences due to the different curvatures of event horizons. As a comparison, we also discuss the topological black holes in the higher dimensional Einstein-Maxwell theory with a negative cosmological constant.