Related papers: Quasilocal conservation laws in cosmology: a first…
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…
We study gravitational properties of vacuum energy by erecting a geometry on the stress-energy tensor of vacuum, matter and radiation. Postulating that the gravitational effects of matter and radiation can be formulated by an appropriate…
Equilibrium thermodynamic laws are typically applied to horizons in general relativity without stating the conditions that bring them into equilibrium. We fill this gap by applying a new thermodynamic interpretation to a generalized…
In [13], a new quasi-local energy is introduced for spacetimes with a non-zero cosmological constant. In this article, we study the small sphere limit of this newly defined quasi-local energy for spacetimes with a negative cosmological…
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…
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 energy of gravitational waves is a fundamental problem in gravity theory. The existing descriptions for the energy of gravitational waves, such as the well-known Isaacson energy-momentum tensor, suffer from several defects. Due to the…
We begin a systematic study of Quantum Energy Inequalities (QEIs) in relation to local covariance. We define notions of locally covariant QEIs of both 'absolute' and 'difference' types and show that existing QEIs satisfy these conditions.…
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…
The M$\o$ller tetrad gravitational energy-momentum expression was recently evaluated for a small vacuum region using orthonormal frames adapted to Riemann normal coordinates. However the result was not proportional to the Bel-Robinson…
Apart from the familiar structure firmly-rooted in the general relativistic field equations where the energy--momentum tensor has a null divergence i.e., it conserves, there exists a considerable number of extended theories of gravity…
We introduce a quasi-local integral functional and scalar quasi-local variables to examine a wide class of spherically symmetric inhomogeneous spacetimes that generalize the Lemaitre-Tolman-Bondi (LTB) dust solutions ("LTB" spacetimes). By…
The problem of defining energy in general relativity is reviewed very briefly, and the properties of Brown-York-like expressions are discussed.
In general relativity, it has been shown that the effective gravitational stress-energy tensor for short-wavelength metric perturbations acts just like that for a radiation fluid, and thus, in particular, cannot provide any effects that…
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…
Asymptotically flat gravitating systems have 10 conserved quantities, which lack proper local densities. It has been hoped that the teleparallel equivalent of Einstein's GR (TEGR, aka GR${}_{||}$) could solve this gravitational…
We take a null hypersurface (the causal horizon) generated by a congruence of null geodesics as the boundary of the Doran-Lobo-Crawford spacetime, to be the place where the Brown-York quasilocal energy is located. The components of the…
A general expression for quasi-local energy flux for spacetime perturbation is derived from covariant Hamiltonian formulation using functional differentiability and symplectic structure invariance, which is independent of the choice of the…
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,…
We construct the Carrollian equivalent of the relativistic energy--momentum tensor, based on variation of the action with respect to the elementary fields of the Carrollian geometry. We prove that, exactly like in the relativistic case, it…