Variational Effect of Boundary Mean Curvature on ADM Mass in General Relativity

Details Variational Effect of Boundary Mean Curvature on ADM Mass in General Relativity Variational Effect of Boundary Mean Curvature on ADM Mass in General Relativity

2003-09-18

arxiv.org/abs/math-ph/0309045v1

Mathematical Physics Research on the Leading Edge, Nova Sci. Publ. NY, 2004, 145--171

Physics

Mathematical Physics

13 pages. This paper is closely related to math-ph/0212025

Scientific paper

We extend the idea and techniques in \cite{Miao} to study variational effect of the boundary geometry on the ADM mass of an asymptotically flat manifold. We show that, for a Lipschitz asymptotically flat metric extension of a bounded Riemannian domain with quasi-convex boundary, if the boundary mean curvature of the extension is dominated by but not identically equal to the one determined by the given domain, we can decrease its ADM mass while raising its boundary mean curvature. Thus our analysis implies that, for a domain with quasi-convex boundary, the geometric boundary condition holds in Bartnik's minimal mass extension conjecture \cite{Bartnik_energy}.

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