Mass of asymptotically flat $3$-manifolds with boundary

Abstract

We study the mass of asymptotically flat $3$-manifolds with boundary using the method of Bray-Kazaras-Khuri-Stern. More precisely, we derive a mass formula on the union of an asymptotically flat manifold and fill-ins of its boundary, and give new sufficient conditions guaranteeing the positivity of the mass. Motivation to such consideration comes from studying the quasi-local mass of the boundary surface. If the boundary isometrically embeds in the Euclidean space, we apply the formula to obtain convergence of the Brown-York mass along large surfaces tending to $\infty$ which include the scaling of any fixed coordinate-convex surface.

arXiv comment30 pages, 2 figures

References in corpus (5)

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• Isometric embeddings into the Minkowski space and new quasi-local mass
• On the positive mass theorem for manifolds with corners
• Boundary conditions at spatial infinity from a Hamiltonian point of view
• Scalar curvature and harmonic one-forms on three-manifolds with boundary

Cited by in corpus (4)

• Spacetime Harmonic Functions and Applications to Mass
• Dihedral rigidity for cubic initial data sets
• On a spacetime positive mass theorem with corners
• Rigidity of Riemannian Penrose inequality with corners and its implications