Dimensionally Continued Black Holes

TL;DR

This work develops a dimensionally continued gravity framework to study static, spherically symmetric black holes with negative cosmological constant, using an AdS-invariant Euler-Chern-Simons form in odd dimensions and a Born-Infeld–like Euler density in even dimensions. It derives exact, charged and uncharged black-hole solutions characterized by mass $M$ and charge $Q$, analyzes horizon structure and causal diagrams across dimensions, and explores asymptotic behaviors (AdS vs. flat) with detailed Penrose diagrams. Thermodynamics is formulated via the Euclidean action and canonical boundary charges, showing entropy as a horizon term $S(r_+)$ and mass/charge from surface fluxes, with temperature and extremality conditions explicitly computed. Overall, the paper connects higher-dimensional Lovelock gravity to AdS/CFT-inspired constructs, providing explicit metrics, thermodynamic relations, and causal structures for dimensionally continued black holes.

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.