Quasilocal Mass in General Relativity

2008/04/30 by Mu-Tao Wang, Mu‐Tao Wang, Shing-Tung Yau +1 · 5 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #gr-qc #math.AP #math.DG

paper · pdf · doi:10.1103/physrevlett.102.021101

published as Phys.Rev.Lett.102:021101,2009 · 10 pages, editorial changes made to comply with journal's page limit, to appear in Physical Review Letters

arxiv created 2008/12/04 · openalex publication_date 2009/01/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

There have been many attempts to define the notion of quasilocal mass for a spacelike two 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 non-negative 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.

Citations

• Positive Mass Theorem and the Boundary Behaviors of Compact Manifolds with Nonnegative Scalar Curvature
• A new proof of the positive energy theorem

Cited by

• Limit of Quasilocal Mass at Spatial Infinity
• Quasi-local energy and the choice of reference
• A Gibbons–Penrose Inequality for Surfaces in Schwarzschild Spacetime
• A note on the post-Newtonian limit of quasi-local energy expressions
• Lifshitz holography

Related

• Quasilocal mass and surface Hamiltonian in spacetime
• A Quasi-Local Mass
• Rigidity and minimizing properties of quasi-local mass
• Quasi-local mass and isometric embedding with reference to a static spacetime
• A proposal of quasi-local mass for 2-surfaces of timelike mean curvature