Extrinsic black hole uniqueness in pure Lovelock gravity

Abstract

We define a notion of extrinsic black hole in pure Lovelock gravity of degree $k$ which captures the essential features of the so-called Lovelock-Schwarzschild solutions, viewed as rotationally invariant hypersurfaces with null $2k$-mean curvature in Euclidean space ${\mathbb{R}}^{n+1}$, $2\le 2k\le n-1$. We then combine a regularity argument with a rigidity result by Araújo-Leite to prove, under a natural ellipticity condition, a global uniqueness theorem for this class of black holes. As a consequence we obtain, in the context of the corresponding Penrose inequality for graphs established by Ge-Wang-Wu, a local rigidity result for the Lovelock-Schwarzschild solutions.

15 pages; no figures; this posting supersedes arXiv:1205.1132; published version

References in corpus (4)

• Black Holes in Pure Lovelock Gravities
• Lovelock's theorem revisited
• Quasi-local energy and ADM mass in pure Lovelock gravity
• The Graphs Cases of the Riemannian Positive Mass and Penrose Inequalities in All Dimensions