Quasi-local energy with respect to a static spacetime

Abstract

This article considers the quasi-local energy in reference to a general static spacetime. We follow the approach developed by the authors in [19, 20, 7, 9] and define the quasi-local energy as a difference of surface Hamiltonians, which are derived from the Einstein-Hilbert action. The new quasi-local energy provides an effective gauge independent measurement of how far a spacetime deviates away from the reference static spacetime on a finitely extended region.

arXiv comment16 pages. arXiv admin note: text overlap with arXiv:1603.02975

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Cited by in corpus (5)

• Minimal hypersurfaces and boundary behavior of compact manifolds with nonnegative scalar curvature
• A rigidity theorem for surfaces in Schwarzschild manifold
• Variation and rigidity of quasi-local mass
• An integral formula for affine connections
• Uniqueness of isometric immersions with the same mean curvature