The Lovelock Black Holes
Cecilia Garraffo, Gaston Giribet
TL;DR
The paper surveys Lovelock gravity as the natural higher-curvature extension of General Relativity in higher dimensions, emphasizing its string-theory origins and second-order field equations. It analyzes five-dimensional black hole solutions, focusing on the Einstein-Gauss-Bonnet sector, the Boulware-Deser metric and its two branches, and the rich horizon and thermodynamic structure that arise, including topological and Chern-Simons variants. It then explores boundary terms and junction conditions that allow vacuum wormholes via geometric surgery, and investigates the quantum regularity of naked singularities using Horowitz–Marolf criteria, highlighting when quantum evolution remains well-defined. Together, these results illustrate how UV corrections qualitatively modify black hole physics, horizon structure, and spacetime topology, with implications for AdS/CFT and holography.
Abstract
Lovelock theory is a natural extension of Einstein theory of gravity to higher dimensions, and it is of great interest in theoretical physics as it describes a wide class of models. In particular, it describes string theory inspired ultraviolet corrections to Einstein-Hilbert action, while admits the Einstein general relativiy and the so called Chern-Simons theories of gravity as particular cases. Recently, five-dimensional Lovelock theory has been considered in the literature as a working example to illustrate the effects of including higher-curvature terms in the context of AdS/CFT correspondence. Here, we give an introduction to the black hole solutions of Lovelock theory and analyze their most important properties. These solutions can be regarded as generalizations of the Boulware-Deser solution of Einstein-Gauss-Bonnet gravity, which we discuss in detail here. We briefly discuss some recent progress in understading these and other solutions, like topological black holes that represent black branes of the theory, and vacuum thin-shell wormhole-like geometries that connect two different asymptotically de-Sitter spaces. We also make some comments on solutions with time-like naked singularities.