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.
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)