### Abstract

Let (M, g) be an asymptotically flat static vacuum initial data set with non-empty compact boundary Σ. We prove that (M, g) is isometric to a spacelike slice of a Schwarzschild spacetime under the mere assumption that Σ has zero mean curvature, hence generalizing a classic result of Bunting and Masood-ul-Alam. In the case that Σ has constant positive mean curvature and satisfies a stability condition, we derive an upper bound of the ADM mass of (M, g) in terms of the mean curvature and area of Σ. Our discussion is motivated by Bartnik's quasi-local mass definition.

Original language | English (US) |
---|---|

Journal | Classical and Quantum Gravity |

Volume | 22 |

Issue number | 11 |

DOIs | |

State | Published - Jun 7 2005 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**A remark on boundary effects in static vacuum initial data sets.** / Miao, Pengzi.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - A remark on boundary effects in static vacuum initial data sets

AU - Miao, Pengzi

PY - 2005/6/7

Y1 - 2005/6/7

N2 - Let (M, g) be an asymptotically flat static vacuum initial data set with non-empty compact boundary Σ. We prove that (M, g) is isometric to a spacelike slice of a Schwarzschild spacetime under the mere assumption that Σ has zero mean curvature, hence generalizing a classic result of Bunting and Masood-ul-Alam. In the case that Σ has constant positive mean curvature and satisfies a stability condition, we derive an upper bound of the ADM mass of (M, g) in terms of the mean curvature and area of Σ. Our discussion is motivated by Bartnik's quasi-local mass definition.

AB - Let (M, g) be an asymptotically flat static vacuum initial data set with non-empty compact boundary Σ. We prove that (M, g) is isometric to a spacelike slice of a Schwarzschild spacetime under the mere assumption that Σ has zero mean curvature, hence generalizing a classic result of Bunting and Masood-ul-Alam. In the case that Σ has constant positive mean curvature and satisfies a stability condition, we derive an upper bound of the ADM mass of (M, g) in terms of the mean curvature and area of Σ. Our discussion is motivated by Bartnik's quasi-local mass definition.

UR - http://www.scopus.com/inward/record.url?scp=21244447037&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21244447037&partnerID=8YFLogxK

U2 - 10.1088/0264-9381/22/11/L01

DO - 10.1088/0264-9381/22/11/L01

M3 - Article

AN - SCOPUS:21244447037

VL - 22

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 11

ER -