### 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 S^{3} 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 S^{n}, with n ≥ 4, such that (S^{n}, g) isometrically embeds into R^{n}
^{+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 language | English (US) |
---|---|

Pages (from-to) | 937-956 |

Number of pages | 20 |

Journal | Mathematical Research Letters |

Volume | 25 |

Issue number | 3 |

State | Published - Jan 1 2018 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Mathematical Research Letters*,

*25*(3), 937-956.

**Higher dimensional black hole initial data with prescribed boundary metric.** / Cabrera Pacheco, Armando J.; Miao, Pengzi.

Research output: Contribution to journal › Article

*Mathematical Research Letters*, vol. 25, no. 3, pp. 937-956.

}

TY - JOUR

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

AU - Cabrera Pacheco, Armando J.

AU - Miao, Pengzi

PY - 2018/1/1

Y1 - 2018/1/1

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.

UR - http://www.scopus.com/inward/record.url?scp=85051263249&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85051263249&partnerID=8YFLogxK

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 -