Related papers: Noether's Theorems and Energy in General Relativit…
We formulate the nonminimal aether-modified gravity whose action represents itself as a sum of the usual Einstein-Hilbert action and the CPT-even Lorentz-breaking aether-like gravity term proposed by Carroll. For this theory, we show that…
According to Einstein's principle of general covariance, all laws of nature are to be expressed by manifestly covariant equations. In recent work, the covariant law of energy-momentum conservation has been established. Here, we show that…
We study the relation between the thermodynamics and field equations of generalized gravity theories on the dynamical trapping horizon with sphere symmetry. We assume the entropy of dynamical horizon as the Noether charge associated with…
We address the problem of the energy conditions in modified gravity taking into account the additional degrees of freedom related to scalar fields and curvature invariants. The latter are usually interpreted as generalized {\it geometrical…
We obtain a generally covariant conservation law of energy-momentum for gravitational anyons by the general displacement transform. The energy-momentum currents have also superpotentials and are therefore identically conserved. It is shown…
Since gravitational wave spacetimes are time-varying vacuum solutions of Einstein's field equations, there is no unambiguous means to define their energy content. However, Weber and Wheeler had demonstrated that they do impart energy to…
Noether symmetry for higher order gravity theory has been explored, with the introduction of an auxiliary variable which gives the only correct quantum desccription of the theory, as shown in a series of earlier papers. The application of…
The Abraham--Minkowski momentum controversy is the outwardly visible symptom of an inconsistency in the use of the energy-momentum tensor in the case of a plane quasimonochromatic field in a simple linear dielectric. We show that the Gordon…
We present a general algorithm constructing a discretization of a classical field theory from a Lagrangian. We prove a new discrete Noether theorem relating symmetries to conservation laws and an energy conservation theorem not based on any…
The connection between symmetries and conservation laws as made by Noether's theorem is extended to the context of causal variational principles and causal fermion systems. Different notions of continuous symmetries are introduced. It is…
We introduce a naturally-defined totally invariant spacetime energy expression for general relativity incorporating the contribution from gravity. The extension links seamlessly to the action integral for the gravitational field. The demand…
When discussing consequences of symmetries of dynamical systems based on Noether's first theorem, most standard textbooks on classical or quantum mechanics present a conclusion stating that a global continuous Lie symmetry implies the…
A proposal for the gravitational energy-momentum tensor, known in the literature as the square root of Bel-Robinson tensor, is analyzed in detail. Being constructed exclusively from the Weyl part of the Riemann tensor, such tensor…
We develop the $n$-dimensional cosmology for $f(\mathcal{G})$ gravity, where $\mathcal{G}$ is the \emph{Gauss-Bonnet} topological invariant. Specifically, by the so-called Noether Symmetry Approach, we select $f(\mathcal{G})\simeq…
Energy-momentum is an important conserved quantity whose definition has been a focus of many investigations in general relativity. Unfortunately, there is still no generally accepted definition of energy and momentum in general relativity.…
There are well-known problems associated with the idea of (local) gravitational energy in general relativity. We offer a new perspective on those problems by comparison with Newtonian gravitation, and particularly geometrized Newtonian…
General Relativity suffers for two main problems which have not yet been overcome: it predicts spacetime singularities and cannot be formulated as a perturbative renormalizable theory. In particular, many attempts have been made for…
This paper is devoted to the investigation of the energy-momentum problem in two theories, i.e., General Relativity and teleparallel gravity. We use Einstein, Landau-Lifshitz, Bergmann-Thomson and M\"{o}ller's prescriptions to evaluate…
These notions in the title are of fundamental importance in any branch of physics. However, there have been great difficulties in finding physically acceptable definitions of them in general relativity since Einstein's time. I shall explain…
A general recipe proposed elsewhere to define, via Noether theorem, the variation of energy for a natural field theory is applied to Einstein-Maxwell theory. The electromagnetic field is analysed in the geometric framework of natural…