Related papers: Quasilocal Energy in General Relativity
In this article, we study the small sphere limit of the Wang-Yau quasi-local energy defined in [18,19]. Given a point $p$ in a spacetime $N$, we consider a canonical family of surfaces approaching $p$ along its future null cone and evaluate…
We discuss our recent work [4] in which gravitational radiation was studied by evaluating the Wang-Yau quasi-local mass of surfaces of fixed size at the infinity of both axial and polar perturbations of the Schwarzschild spacetime, \`{a} la…
The specification of energy for gravitating systems has been an unsettled issue since Einstein proposed his pseudotensor. It is now understood that energy-momentum is \emph{quasi-local} (associated with a closed 2-surface). Here we consider…
In this article, we compute the limit of the Wang--Yau quasi-local mass on a family of surfaces approaching the apparent horizon (the near horizon limit). Such limit is first considered in [1]. Recently, Pook-Kolb, Zhao, Andersson,…
Bartnik's definition of gravitational quasilocal energy is analyzed. For a wide class of systems Bartnik's function is given by the ADM mass of some vacuous extension. As an example we calculate mass of a non central ball in Schwarzschild…
In this paper, we show that the Chen-Nester-Tung (CNT) quasi-local energy is closely related to the Wang-Yau (WY) quasi-local mass. As a particular example, we compute the second variation of the CNT quasi-local energy for axially symmetric…
We discuss the concepts of energy and mass in relativity. On a finitely extended spatial region, they lead to the notion of quasilocal energy/mass for the boundary 2-surface in spacetime. A new definition was found in [27] that satisfies…
A definition of quasi-local energy in a gravitational field based upon its embedding into flat space is discussed. The outcome is not satisfactory from many points of view.
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…
In this paper, we prove the following theorem regarding the Wang-Yau quasi-local energy of a spacelike two-surface in a spacetime: Let $\Sigma$ be a boundary component of some compact, time-symmetric, spacelike hypersurface $\Omega$ in a…
With the aid of a simple family of examples, we show that the quasi-local mass defined by Kijowski and Liu and Yau, and shown by Liu and Yau to be positive, may be strictly positive for space-like, topologically spherical 2-surfaces in flat…
Motivated by the important work of Brown adn York on quasilocal energy, we propose definitions of quasilocal energy and momentum surface energy of a spacelike 2-surface with positive intrinsic curvature in a spacetime. We show that the…
In this paper, we obtain a positivity result of a quasi-local mass integral as proposed by Shi and Tam in general dimensions. The main argument is based on the monotonicity of a mass integral in a foliation of quasi-spherical metrics and a…
A quasi-local energy for Einstein's general relativity is defined by the value of the preferred boundary term in the covariant Hamiltonian formalism. The boundary term depends upon a choice of reference and a time-like displacement vector…
A dynamically preferred quasi-local definition of gravitational energy is given in terms of the Hamiltonian of a `2+2' formulation of general relativity. The energy is well-defined for any compact orientable spatial 2-surface, and depends…
A new generalization of the Hawking-Hayward quasilocal energy to scalar-tensor gravity is proposed without assuming symmetries, asymptotic flatness, or special spacetime metrics. The procedure followed is simple but powerful and consists of…
The problem of quasilocal energy has been extensively studied mainly in four dimensions. Here we report results regarding the quasilocal energy in spacetime dimension $n\geq 4$. After generalising three distinct quasilocal energy…
An `effective' quasi-local energy expression, motivated by the (relativistically corrected) Newtonian theory, is introduced in exact GR as the volume integral of all the source terms in the field equation for the Newtonian potential in…
In this article, we survey recent developments in defining the quasi-local mass in general relativity. We discuss various approaches and the properties and applications of the different definitions. Among the expected properties, we focus…
In general relativity, the local gravitational energy is best characterised by the quasilocal mass. The small sphere limit of quasilocal mass provides us the most local notion of gravitational energy. In four dimensions, the limits were…