Related papers: Quasi-local mass at null infinity in Bondi-Sachs c…
In the Bondi-Sachs formulation of General Relativity space-time is foliated via a family of null cones. If these null cones are defined such that their vertices are traced by a regular world-line then the metric tensor has to obey…
We consider smooth null cones in a vacuum spacetime that extend to future null infinity. For such cones that are perturbations of shear-free outgoing null cones in Schwarzschild spacetimes, we prove bounds for the Bondi energy, momentum,…
We define the energy of a perfectly isolated system at a given retarded time as the suitable null limit of the quasilocal energy $E$. The result coincides with the Bondi-Sachs mass. Our $E$ is the lapse-unity shift-zero boundary value of…
A set of exact quasi-local conservation equations is derived from the Einstein's equations using the first-order Kaluza-Klein formalism of general relativity in the (2,2)-splitting of 4-dimensional spacetime. These equations are interpreted…
When a system emits gravitational radiation, the Bondi mass decreases. If the Bondi energy is Hamiltonian, it can thus only be a time dependent Hamiltonian. In this paper, we show that the Bondi energy can be understood as a time-dependent…
In this paper lower bounds are obtained for quasi-local masses in terms of charge, angular momentum, and horizon area. In particular we treat three quasi-local masses based on a Hamiltonian approach, namely the Brown-York, Liu-Yau, and…
We review Wang-Yau quasi-local definitions along the line of gravitational Hamiltonian. This makes clear the connection and difference between Wang-Yau definition and Brown-York or even global ADM definition. We make a brief comment on…
In this paper we calculate the Bondi mass of asymptotically flat spacetimes with interacting electromagnetic and scalar fields. The system of coupled Einstein-Maxwel-Klein-Gordon equations is investigated and corresponding field equations…
We show that the quasilocal mass defined by Wang and Yau is not well-defined at spatial infinity. It approaches neither the ADM mass nor the ADM energy. We suggest an alternative scheme which retains all the desirable characteristics of the…
In the Bondi formulation of the axisymmetric vacuum Einstein equations, we argue that the ``surface area'' coordinate condition determining the ``radial'' coordinate can be considered as part of the initial data and should be chosen in a…
We define the asymptotic flatness and discuss asymptotic symmetry at null infinity in arbitrary dimensions using the Bondi coordinates. To define the asymptotic flatness, we solve the Einstein equations and look at the asymptotic behavior…
We investigate properties of a quasi-local mass in a higher-dimensional spacetime having symmetries corresponding to the isomertries of an $(n-2)$-dimensional maximally symmetric space in Einstein-Gauss-Bonnet gravity in the presence of a…
We prove the following stronger verson of the positivity of quasi-local mass stated in gr-qc/0303019: the quasi-local energy (mass) of each connected component of the boundary of a compact spacelike hypersurface which satisfies the local…
We study the limit of quasilocal mass defined in [4] and [5] for a family of spacelike 2-surfaces in spacetime. In particular, we show the limit coincides with the ADM mass at spatial infinity. The limit for coordinate spheres of a boosted…
We prove that the Bondi mass of an asymptotically flat, vacuum, spacetime cannot become negative in any even dimension $d \ge 4$. The notion of Bondi mass is more subtle in $d > 4$ dimensions because radiating metrics have a slower decay…
In a vacuum spacetime equips with the Bondi's radiating metric which is asymptotically flat at spatial infinity including gravitational radiation ({\bf Condition D}), we establish the relation between the ADM total linear momentum and the…
We study a functional on the boundary of a compact Riemannian 3-manifold of nonnegative scalar curvature. The functional arises as the second variation of the Wang-Yau quasi-local energy in general relativity. We prove that the functional…
The energy at null infinity is presented with the help of a simple example of a massless scalar field in Minkowski spacetime. It is also discussed for Einstein gravity. In particular, various aspects of the loss of the energy in the…
We find two conditions related to the {\it news functions} of the Bondi's radiating vacuum spacetimes. We provide a complete proof of the positivity of the Bondi mass by using Schoen-Yau's method under one condition and by using Witten's…
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…