相关论文: Quasi-local energy and the choice of reference

We present two complementary approaches for determining the reference for the covariant Hamiltonian boundary term quasi-local energy and test them on spherically symmetric spacetimes. On the one hand, we isometrically match the 2-surface…

For a given timelike displacement vector the covariant Hamiltonian quasi-local energy expression requires a proper choice of reference spacetime. We propose a program for determining the reference by embedding a neighborhood of the…

We have proposed a program for determining the reference for the quasi-local energy defined in the covariant Hamiltonian formalism. Our program has been tested by applying it to the spherically symmetric spacetimes. With respect to…

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…

First we briefly review our covariant Hamiltonian approach to quasi-local energy, noting that the Hamiltonian-boundary-term quasi-local energy expressions depend on the chosen boundary conditions and reference configuration. Then we present…

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…

From a covariant Hamiltonian formulation, by using symplectic ideas, we obtain certain covariant boundary expressions for the quasilocal quantities of general relativity and other geometric gravity theories. The contribution from each of…

The Hamiltonian for a gravitating region includes a boundary term which determines not only the quasi-local values but also, via the boundary variation principle, the boundary conditions. Using our covariant Hamiltonian formalism, we found…

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…

From a covariant Hamiltonian formulation, using symplectic ideas, we obtain covariant quasilocal energy-momentum boundary expressions for general gravity theories. The expressions depend upon which variables are fixed on the boundary, a…

The energy of gravitating systems has been an issue since Einstein proposed general relativity: considered to be ill defined, having no proper local density. Energy-momentum is now regarded as \emph{quasi-local} (associated with a closed…

The boundary term of the gravitational Hamiltonian can be used to give the values of the quasi-local quantities as long as one can provide a suitable evolution vector field and an appropriate reference. On the two-surface boundary of a…

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 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…

The Hamiltonian for dynamic geometry generates the evolution of a spatial region along a vector field. It includes a boundary term which determines both the value of the Hamiltonian and the boundary conditions. The value gives the…

Energy is at best defined quasilocally in general relativity. Quasilocal energy definitions depend on the conditions one imposes on the boundary Hamiltonian, i.e., how a finite region of spacetime is "isolated". Here, we propose a method to…

Traditional approaches to energy-momentum localization led to reference frame dependent pseudotensors. The more modern idea is quasilocal energy-momentum. We take a Hamiltonian approach. The Hamiltonian boundary term gives not only the…

In this paper, by arising condition in variation, from equal time to non-equal time, I reconsider how geometrodynamics equations allow to be derived from variational principle in general relativity and then find the variation of extrinsic…

I describe the Einstein's gravitation of 3+1 dimensional spacetimes using the (2,2) formalism without assuming isometries. In this formalism, quasi-local energy, linear momentum, and angular momentum are identified from the four Einstein's…

The quasi-local energy conservation law is derived from the vacuum Einstein's equations on the timelike boundary surface in the canonical (2,2)-formalism of general relativity. The quasi-local energy and energy flux integral agree with the…