A Remark on Boundary Effects in Static Vacuum Initial Data sets

Details A Remark on Boundary Effects in Static Vacuum Initial Data sets A Remark on Boundary Effects in Static Vacuum Initial Data sets

2005-04-19

arxiv.org/abs/gr-qc/0504081v1

Class.Quant.Grav. 22 (2005) L53-L59

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages, to be published in Classical and Quantum Gravity

Scientific paper

10.1088/0264-9381/22/11/L01

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

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