Higher dimensional black hole initial data with prescribed boundary metric

Armando J. Cabrera Pacheco, Pengzi Miao

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

We obtain higher dimensional analogues of the results of Mantoulidis and Schoen in [8]. More precisely, we show that (i) any metric g with positive scalar curvature on the 3-sphere S3 can be realized as the induced metric on the outermost apparent horizon of a 4-dimensional asymptotically flat manifold with non-negative scalar curvature, whose ADM mass can be arranged to be arbitrarily close to the optimal value specified by the Riemannian Penrose inequality; (ii) any metric g with positive scalar curvature on the n-sphere Sn, with n ≥ 4, such that (Sn, g) isometrically embeds into Rn +1 as a star-shaped hypersurface, can be realized as the induced metric on the outermost apparent horizon of an (n + 1)-dimensional asymptotically flat manifold with non-negative scalar curvature, whose ADM mass can be made to be arbitrarily close to the optimal value.

Original languageEnglish (US)
Pages (from-to)937-956
Number of pages20
JournalMathematical Research Letters
Volume25
Issue number3
StatePublished - Jan 1 2018

ASJC Scopus subject areas

  • Mathematics(all)

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