Quasilocal Mass in General Relativity

Wang, Mu-Tao; Yau, Shing–Tung

doi:10.1103/physrevlett.102.021101

Cited by 219 publications

(325 citation statements)

References 20 publications

Supporting

Mentioning

317

Contrasting

Order By: Relevance

“…Finally most all of the discussion below applies also to more recent modifications of the BY approach by several authors, cf. [5]- [8]; however again for clarity and simplicity we focus on the Brown-York Hamiltonian and leave it to the reader to extend the analysis to the more recent alternatives.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Quasilocal Hamiltonians in general relativity

Anderson¹

2010

Phys. Rev. D

View full text Add to dashboard Cite

Abstract. We analyse the definition of quasi-local energy in GR based on a Hamiltonian analysis of the Einstein-Hilbert action initiated by Brown-York. The role of the constraint equations, in particular the Hamiltonian constraint on the timelike boundary, neglected in previous studies, is emphasized here. We argue that a consistent definition of quasi-local energy in GR requires, at a minimum, a framework based on the (currently unknown) geometric well-posedness of the initial boundary value problem for the Einstein equations.The analysis of the gravitational field by Arnowitt-Deser-Misner [1] has led to a clear and welldefined construction of the Hamiltonian, and resulting definitions of energy, linear and angular momentum in the context of asymptotically flat spacetimes. These concepts are obviously of basic importance in understanding the physics of such (infinite) isolated gravitating systems. Nevertheless, infinite systems are idealizations of more realistic physical situations, and it is desirable to have available a similar analysis in the case of physical systems of finite extent.However the understanding of this issue for domains of finite extent is much less satisfactory. Despite numerous proposals, from a number of different viewpoints, a consensus has not yet been reached on a suitable definition of the Hamiltonian or energy of a finite system, i.e. a quasi-local Hamiltonian; cf.[2] for an excellent detailed survey of the current state of the art.In this paper, we first examine and comment on the approach to the definition of energy of a finite region of spacetime based on the Hamiltonian formulation of GR. This is essentially based on a localization of the approach taken by ADM [1] and Regge-Teitelboim [3], keeping careful track of the boundary terms that arise in a Hamiltonian or Hamilton-Jacobi analysis. This approach was initiated and pioneered by Brown-York (BY) [4]. To keep the discussion focused on the central issue, we only consider the gravitational field, (so other matter fields are set to zero); in addition, we consider only the energy and not related concepts such as linear and angular momentum, although this could be done without undue difficulty. Finally most all of the discussion below applies also to more recent modifications of the BY approach by several authors, cf.[5]-[8]; however again for clarity and simplicity we focus on the Brown-York Hamiltonian and leave it to the reader to extend the analysis to the more recent alternatives.We first recall the set-up. Let M be a spacetime region, topologically of the form I × Σ, with I = [0, 1] parametrizing time and Σ a compact 3-manifold with boundary S; typically S = ∂Σ is a 2-sphere and Σ a 3-ball. The boundary ∂M of M is a union of two spatial hypersurfaces Σ 0 ∪ Σ 1 and the timelike boundary T = I × ∂S = ∪S t . These boundaries meet at the seams or corners S 0 and S 1 . The Einstein-Hilbert action is then given by (setting 8πG = 1),where g is a smooth Lorentz metric on M . The Hamiltonian in GR plays two important but a priori distin...

show abstract

mentioning

confidence: 99%

“…First, the definition of the BY Hamiltonian, as well as its more recent modifications [5]- [8] require a choice of subtraction term to normalize the zero-point of the energy. These subtraction terms are typically determined by choices of isometric embedding of (S, γ S ) into either Euclidean space R 3 or Minkowski space R 1,3 .…”

mentioning

confidence: 99%

Quasilocal Hamiltonians in general relativity

Anderson¹

2010

Phys. Rev. D

View full text Add to dashboard Cite

show abstract

“…The energy (2.3) satisfies the important positivity and rigidity properties by the work of [47,48], see also [44,31].…”

Section: The New Definitionmentioning

confidence: 99%

Energy, momentum, and center of mass in general relativity

Wang

2016

Surveys in Differential Geometry

Self Cite

View full text Add to dashboard Cite

Abstract. These notions in the title are of fundamental importance in any branch of physics. However, there have been great difficulties in finding physically acceptable definitions of them in general relativity since Einstein's time. I shall explain these difficulties and progresses that have been made. In particular, I shall introduce new definitions of center of mass and angular momentum at both the quasi-local and total levels, which are derived from first principles in general relativity and by the method of geometric analysis. With these new definitions, the classical formula p = mv is shown to be consistent with Einstein's field equation for the first time. This paper is based on joint work [14,15] with Po-Ning Chen and Shing-Tung Yau.

show abstract

“…For nonstationary fields where there is an asymptotic time translation symmetry, one can define the Bondi energy at null infinity. Since we usually work in a nonisolated system, for convenience, several quasilocal mass definitions have been constructed [1,2]. If we consider cases with more symmetry, it is obvious that most of these definitions become equivalent to each other and the Misner-Sharp mass is normally a well-posed one [3].…”

Section: Introductionmentioning

confidence: 99%

Mass inflation and curvature divergence near the central singularity in spherical collapse

2015

View full text Add to dashboard Cite

We study spherical scalar collapse toward a black hole formation and examine the asymptotic dynamics near the central singularity of the formed black hole. It is found that, in the vicinity of the singularity, due to the strong backreaction of a scalar field on the geometry, the mass function inflates and the Kretschmann scalar grows faster than in the Schwarzschild geometry. In collapse, the Misner-Sharp mass is a locally conserved quantity, not providing information on the black hole mass that is measured at asymptotically flat regions.

show abstract

Quasilocal Mass in General Relativity

Cited by 219 publications

References 20 publications

Quasilocal Hamiltonians in general relativity

Quasilocal Hamiltonians in general relativity

Energy, momentum, and center of mass in general relativity

Mass inflation and curvature divergence near the central singularity in spherical collapse

Contact Info

Product

Resources

About