Related papers: Quasilocal mass and surface Hamiltonian in spaceti…

Two locally positive expressions for the gravitational Hamiltonian, one using 4-spinors the other special orthonormal frames, are reviewed. A new quadratic 3-spinor-curvature identity is used to obtain another positive expression for the…

This paper presents a complete set of quasilocal densities which describe the stress-energy-momentum content of the gravitational field and which are built with Ashtekar variables. The densities are defined on a two-surface $B$ which bounds…

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…

A recent generalization of the Hawking-Hayward quasilocal energy to scalar-tensor gravity is adapted to general spherically symmetric geometries. It is then applied to several black hole and other spherical solutions of scalar-tensor and…

Our topic concerns a long standing puzzle: the energy of gravitating systems. More precisely we want to consider, for gravitating systems, how to best describe energy-momentum and angular momentum/center-of-mass momentum (CoMM). It is known…

The Hamiltonian of a gravitational system defined in a region with boundary is quantized. The classical Hamiltonian, and starting point for the regularization, is required by functional differentiablity of the Hamiltonian constraint. The…

We derive a formula describing the transformation of the Hawking-Hayward quasi-local energy under a conformal rescaling of the spacetime metric. A known formula for the transformation of the Misner-Sharp-Hernandez mass is recovered as a…

We consider an isolated system made of two pointlike bodies interacting at a distance in the nonradiative approximation. Our framework is the covariant and a priori Hamiltonian formalism of "predictive relativistic mechanics", founded on…

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…

We give a brief review of the definition of the Wang-Yau quasilocal mass and discuss the evaluation of which on surfaces of unit size at null infinity of an axi-symmetric spacetime in Bondi-van der Burg-Metzner coordinates.

We define the (total) center of mass for suitably asymptotically hyperbolic time-slices of asymptotically anti-de Sitter spacetimes in general relativity. We do so in analogy to the picture that has been consolidated for the (total) center…

Casimir energy in presence of a weak gravitational field is discussed taking into account the issues related to energy and its conservation in a curved background. It is well-known that there are inherent difficulties in defining energy in…

Jeffrey and Kirwan suggested expressions for intersection pairings on the reduced space of a Hamiltonian G-space in terms of multiple residues. In this paper we prove a residue formula for symplectic volumes of reduced spaces of a…

Wang and Yau [10] introduced a quasi-local mass, which is a hyperbolic background generalization of Liu-Yau's expression [7] [8], and proved its positivity. In this note, we prove that the positivity of this quasi-local mass is still valid…

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…

The quasilocal energy associated with a constant stationary time slice of the Kerr spacetime is presented. The calculations are based on a recent proposal \cite{by} in which quasilocal energy is derived from the Hamiltonian of spatially…

We first describe a class of spinor-curvature identities (SCI) which have gravitational applications. Then we sketch the topic of gravitational energy-momentum, its connection with Hamiltonian boundary terms and the issues of positivity and…

Entropy and energy are found to be closely tied on our quest for quantum gravity. We point out an interesting connection between the recently proposed outer entropy, a coarse-grained entropy defined for a compact spacetime domain motivated…

We identify a condition on spacelike 2-surfaces in a spacetime that is relevant to understanding the concept of mass in general relativity. We prove a formula for the variation of the spacetime Hawking mass under a uniformly area expanding…

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…