TY - JOUR

T1 - Higher dimensional black hole initial data with prescribed boundary metric

AU - Cabrera Pacheco, Armando J.

AU - Miao, Pengzi

N1 - Funding Information:
The work of AJCP was partially supported by the National Council of Science and Technology of Mexico (CONACyT). The work of PM was partially supported by a Simons Foundation Collaboration Grant for Mathematicians #281105. We sincerely thank the anonymous referee whose insightful comment led to the improvement of Theorem 1.1. We also give our deepest thanks to F. C. Marques for suggesting the proof of Proposition 2.1.
Publisher Copyright:
© 2018 International Press of Boston Inc. All rights reserved.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

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U2 - 10.4310/MRL.2018.v25.n3.a10

DO - 10.4310/MRL.2018.v25.n3.a10

M3 - Article

AN - SCOPUS:85051263249

VL - 25

SP - 937

EP - 956

JO - Mathematical Research Letters

JF - Mathematical Research Letters

SN - 1073-2780

IS - 3

ER -