Topological black holes in the dimensionally continued gravity

TL;DR

This work analyzes topological black holes in dimensionally continued gravity, a Lovelock-based theory that splits into odd and even dimensions with Chern-Simons AdS and Euler-density Lagrangians, respectively. It derives static, spherically symmetric solutions whose event horizons have constant curvature $k\in\{1,0,-1\}$ and computes their Hawking temperatures, entropies (via the first law) and heat capacities, showing that entropy generally deviates from the area law and depends on dimension parity. The study covers uncharged and electrically charged cases, revealing distinct thermodynamic behaviors: odd-dimensional black holes have positive heat capacity and stable thermodynamics, while even-dimensional cases can exhibit phase-transition-like features; charging introduces RN-AdS–type structures and modifies stability via $C_Q$. The results highlight the crucial role of horizon topology and spacetime dimension in the thermodynamics of higher-curvature gravity theories and have potential implications for AdS/CFT and holography in nontrivial topologies.

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.