Extrinsic black hole uniqueness in pure Lovelock gravity
| Autor: | de Lima, Levi Lopes, Girão, Frederico, Natário, José |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Bulletin of the Brazilian Mathematical Society, New Series (2021) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00574-021-00279-0 |
| Popis: | 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. Comment: 15 pages; no figures; this posting supersedes arXiv:1205.1132; published version |
| Databáze: | arXiv |
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