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arXiv · 2107.03037

Extrinsic black hole uniqueness in pure Lovelock gravity

Levi Lopes de Lima·Frederico Girão·José Natário
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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 $\mathbb R^{n+1}$, $2\leq 2k\leq n-1$. We then combine a regularity argument with a rigidity result by Ara\'ujo-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.

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BibTeXRIS

Levi Lopes de Lima, Frederico Girão, José Natário. 2021-07-07. Extrinsic black hole uniqueness in pure Lovelock gravity. https://doi.org/10.1007/s00574-021-00279-0

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