Related papers: Quasi-local definitions of energy in general relat…
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…
Whether energy is conserved in a universe which keeps expanding is an intriguing question. It is tempting to argue that the total energy within the universe would have to increase as the universe expands. Upon more detailed inspection the…
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.
It is shown that under proper conditions in an appropriate coordinate system with a suitable time slicing the Hamiltonian and the Einstein-Hilbert action including all necessary boundary terms can be written on shell in terms of the…
We construct a Hamiltonian formulation of quasilocal general relativity using an extended phase space that includes boundary coordinates as configuration variables. This allows us to use Hamiltonian methods to derive an expression for the…
Pointlike objects cause many of the divergences that afflict physical theories. For instance, the gravitational binding energy of a point particle in Newtonian mechanics is infinite. In general relativity, the analog of a point particle is…
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…
I give a brief review of the search for a proper definition of energy in General Relativity (GR), a far from trivial quest, which was only completed after four and a half decades. The equally (or perhaps more) difficult task of establishing…
The Brown-York quasi-local energy of a rotating black hole described by the Kerr metric and enclosed by a fixed-radius surface is calculated by direct computation. No special assumptions on the angular momentum or the radial coordinate in…
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 standard candidate for quasilocal energy in general relativity is the Brown-York energy, which is essentially a two dimensional surface integral of the extrinsic curvature on the two-boundary of a spacelike hypersurface referenced to flat…
Although there is no known meaningful notion of the energy density of the gravitational field in general relativity, a few notions of quasi-local energy of gravity associated to extended but finite domains have been proposed. In this paper,…
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…
Recent advances in quantum thermodynamics have been focusing on ever more elementary systems of interest, approaching the limit of a single qubit, with correlations, strong coupling and non-equilibrium environments coming into play. Under…
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…
One usually defines the Brown-York energy for a 2-surface embedded in a spacelike 3-slice as an integration of the mean curvature of the 2-surface isometrically embedded into the 3-slice, with a proper reference 3-space. We demonstrate that…
This paper presents a calculation of the quasilocal energy of a generic FRW model of the universe. The results have the correct behavior in the small-sphere limit and vanish for the empty Milne universe. Higher order corrections are found…
The aim of this chapter is to present an introduction and also an overview of some of the most relevant results concerning positivity energy theorems in General Relativity. These theorems provide the answer to a long standing problem that…
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…
The Brown-York quasi-local energy of a charged rotating black hole described by the Kerr-Newman metric and enclosed by a fixed-radius surface is computed. No further assumptions on the angular momentum or the radial coordinate in…