Year: 2005
Type: article
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.
Source: Classical and Quantum Gravity
Author: Pengzi Miao
Institution: University of California, Santa Barbara
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2002261335