Quasilocal mass in general relativity

Abstract

There have been many attempts to define the notion of quasilocal mass for a spacelike 2-surface in spacetime by the Hamilton-Jacobi analysis. The essential difficulty in this approach is to identify the right choice of the background configuration to be subtracted from the physical Hamiltonian. Quasilocal mass should be nonnegative for surfaces in general spacetime and zero for surfaces in flat spacetime. In this letter, we propose a new definition of gauge-independent quasilocal mass and prove that it has the desired properties.

10 pages, editorial changes made to comply with journal's page limit, to appear in Physical Review Letters

References in corpus (10)

• Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
• The Gravitational Hamiltonian, Action, Entropy, and Surface Terms
• Positivity of Quasilocal Mass
• Moving Observers, Non-orthogonal Boundaries, and Quasilocal Energies
• Collapsing Shells and the Isoperimetric Inequality for Black Holes
• Canonical Quasilocal Energy and Small Spheres
• Lightcone reference for total gravitational energy
• Angular momentum and an invariant quasilocal energy in general relativity
• A comment on Liu and Yau's positive quasi-local mass
• The Liu-Yau mass as a good quasi-local energy in general relativity

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