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 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
Higher dimensional black hole initial data with prescribed boundary metric. / Cabrera Pacheco, Armando J.; Miao, Pengzi.
In: Mathematical Research Letters, Vol. 25, No. 3, 01.01.2018, p. 937-956.Research output: Contribution to journal › Article
}
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 -