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 and Leite (Indiana University Mathematics Journal pp. 1667–1693, 2012) 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 et al. (Advances in Mathematics 266: 84–119, 2014), a local rigidity result for the Lovelock-Schwarzschild solutions.
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L.L. de Lima has been partially supported by CNPq/Brazil grant 312485/2018-2, F. Girão by CNPq/Brazil grant 307239/2020-9 and J. Natário by FCT/Portugal grant UIDP/MAT/04459/2020 The authors have also benefited from support coming from FUNCAP/CNPq/PRONEX grant 00068.01.00/15.
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de Lima, L.L., Girão, F. & Natário, J. Extrinsic Black Hole Uniqueness in Pure Lovelock Gravity. Bull Braz Math Soc, New Series 53, 721–739 (2022). https://doi.org/10.1007/s00574-021-00279-0
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DOI: https://doi.org/10.1007/s00574-021-00279-0