Related papers: Is energy conserved in general relativity ?
We will read, through the Emmy Noether paper and the two concepts of `proper' and `improper' conservation laws, the problem, posed by Hilbert, of the nature of the law of conservation of energy in the theory of General Relativity.…
In an expanding universe the vacuum energy density \rho_{\Lambda} is expected to be a dynamical quantity. In quantum field theory in curved space-time \rho_{\Lambda} should exhibit a slow evolution, determined by the expansion rate of the…
The energy localization hypothesis of the author that energy is localized in non-vanishing regions of the energy-momentum tensor implies that gravitational waves do not carry energy in vacuum. If substantiated, this has significant…
We construct the gravitational energy-momentum tensor in general relativity through the Noether theorem. In particular, we explicitly demonstrate that the constructed quantity can vary as a tensor under the general coordinate…
This report offers a modern perspective on the problem of negative energy, based on a re-examination of the concept of time direction as it arises in a classical and quantum-mechanical context. From this analysis emerges an improved…
Energy conservation has the status of a fundamental physical principle. However, measurements in quantum mechanics do not comply with energy conservation. Therefore, it is expected that a more fundamental theory of gravity -- one that is…
In General Relativity, the issue of defining the gravitational energy contained in a given spatial region is still unresolved, except for particular cases of localized objects where the asymptotic flatness holds for a given spacetime. In…
Recently, the author and collaborators proposed a method to construct a new conserved charge different from the Noether one for general relativistic field theory on curved space-time with energy-momentum tensor covariantly conserved, and…
The generalized Stokes theorem (connecting integrals of dimensions 3 and 4) is formulated in a curved space-time in terms of paths in Minkowski space (forming Path Group). A covariant integral form of the conservation law for the…
We discuss general properties of the conservation law associated with a local symmetry. Using Noether's theorem and a generalized Belinfante symmetrization procedure in 3+1 dimensions, a symmetric energy-momentum (pseudo) tensor for the…
Backgrounds are pervasive in almost every application of general relativity. Here we consider the Lagrangian formulation of general relativity for large perturbations with respect to a curved background spacetime. We show that Noether's…
The debate on conservation laws in general relativity eighty years ago is reviewed and restudied. The physical meaning of the identities in the conservation laws for matter plus gravitational field is reexamined and new interpretations for…
$f(R,T)$ gravity was proposed as an extension of the $f(R)$ theories, containing not just geometrical correction terms to the General Relativity equations, but also material correction terms, dependent on the trace of the energy-momentum…
In some cases, it is possible to show the conservation of energy by using equations of motion in mechanics. By considering these results, some people can think that the conservation of energy is the result of equations of motion or Newton's…
Energy has an ambiguous status in general relativity. For systems embedded in asymptotically flat space-times it is possible to construct an integral invariant that corresponds to total energy, however there is no local differential…
We complete the program of spectral geometry, in the sense that we show that a manifold's shape, i.e., its metric, can be reconstructed from its resonant sound when tapped lightly, i.e., from its spectrum, -- if in addition we also record…
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…
We review the energy concept in the case of a continuum or a system of fields. First, we analyze the emergence of a true local conservation equation for the energy of a continuous medium, taking the example of an isentropic continuum in…
We provide an improved definition of new conserved quantities derived from the energy-momentum tensor in curved spacetime by introducing an additional scalar function. We find that the conserved current and the associated conserved charge…
A problem in general relativity is, how the gravitational field can transfer energy and momentum between different distant places. The issue is that matter stress tensor is locally conserved, with no explicit interaction with the free…