Dimensionally Continued Black Holes

TL;DR

This paper explores black hole solutions in higher-dimensional gravity theories derived from Lovelock actions, revealing their properties, causal structures, and the conditions needed for their existence in various dimensions.

Contribution

It introduces exact black hole solutions in dimensionally continued gravity theories, extending known results to odd and even dimensions with detailed causal analysis.

Findings

Black holes exist in both odd and even dimensions with specific conditions.

Causal structures and Penrose diagrams are characterized for these black holes.

Solutions reduce to known Einstein gravity cases in lower dimensions.

Abstract

Static, spherically symmetric solutions of the field equations for a particular dimensional continuation of general relativity with negative cosmological constant are studied. The action is, in odd dimensions, the Chern-Simons form for the anti-de Sitter group and, in even dimensions, the Euler density constructed with the Lorentz part of the anti-de Sitter curvature tensor. Both actions are special cases of the Lovelock action, and they reduce to the Hilbert action (with negative cosmological constant) in the lower dimensional cases $\mbox{$\cal D$}=3$ and $\mbox{$\cal D$}=4$. Exact black hole solutions characterized by mass ($M$) and electric charge ($Q$) are found. In odd dimensions a negative cosmological constant is necessary to obtain a black hole, while in even dimensions, both asymptotically flat and asymptotically anti-de Sitter black holes exist. The causal structure is analyzed and the Penrose diagrams are exhibited.