Related papers: Quasilocal angular momentum and center of mass in …
We define quasi-local conserved quantities in general relativity by using the optimal isometric embedding in [26] to transplant Killing fields in the Minkowski spacetime back to the 2-surface of interest in a physical spacetime. To each…
In this article, we consider the limit of quasi-local conserved quantities [31,9] at the infinity of an asymptotically hyperbolic initial data set in general relativity. These give notions of total energy-momentum, angular momentum, and…
We modify previous quasi-local mass definition. The new definition provides expressions of the quasi-local energy, the quasi-local linear momentum and the quasi-local mass. And they are equal to the ADM expressions at spatial infinity.…
A quasi-local mass, typically defined as an integral over a spacelike $2$-surface $\Sigma$, should encode information about the gravitational field within a finite, extended region bounded by $\Sigma$. Therefore, in attempts to quantize…
In general relativity, an idealized distant observer is situated at future null infinity where light rays emitted from the source approach. This article concerns conserved quantities such as mass, energy-momentum, angular momentum, and…
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…
We calculate the limits of the quasi-local angular momentum and center-of-mass defined by Chen-Wang-Yau \cite{CWY} for a family of spacelike two-spheres approaching future null infinity in an asymptotically flat spacetime admitting a…
A set of exact quasi-local conservation equations is obtained in the (1+1)-dimensional description of the Einstein's equations of (3+1)-dimensional spacetimes. These equations are interpreted as quasi-local energy, linear momentum, and…
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…
This article considers the quasi-local conserved quantities with respect to a reference spacetime with a cosmological constant. We follow the approach developed by the authors in [25,26,7] and define the quasi-local energy as differences of…
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…
Gravitating systems have no well-defined local energy-momentum density. Various quasilocal proposals have been made, however the center-of-mass moment (COM) has generally been overlooked. Asymptotically flat graviating systems have 10 total…
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 present an introduction to mass and angular momentum in General Relativity. After briefly reviewing energy-momentum for matter fields, first in the flat Minkowski case (Special Relativity) and then in curved spacetimes with or without…
A new definition of quasi--local angular momentum of non--axisymmetric marginally outer trapped surfaces is proposed. It is based on conformal decomposition of the two--dimensional metric and the action of the group of conformal symmetries.…
Generalized definitions for angular and linear momentum are given and shown to reduce to the ADM (at spatial infinity) definitions and the definitions at null infinity in the appropriate limit. These definitions are used to express angular…
Using the Noether Charge formulation, we study a perturbation of the conserved gravitating system. By requiring the boundary term in the variation of the Hamiltonian to depend only on the symplectic structure, we propose a general…
This article considers the quasi-local energy in reference to a general static spacetime. We follow the approach developed by the authors in [19, 20, 7, 9] and define the quasi-local energy as a difference of surface Hamiltonians, which are…
We study the previously proposed quasilocal angular momentum of gravitational fields in the absence of isometries. The quasilocal angular momentum $L(\xi)$ has the following attractive properties; ({\it i}) it follows from the Einstein's…
In the framework of the quasigroup approach to conservation laws in general relativity, we show how the infinite-parametric Newman-Unti group of asymptotic symmetries can be reduced to the Poincare quasigroup. We compute Noether's charges…