Related papers: The Bel-Robinson tensor and the classical pseudote…
We exploit once again the analogy between the energy-momentum tensor and the so-called ``superenergy'' tensors in order to build conserved currents in the presence of Killing vectors. First of all, we derive the divergence-free property of…
A general affine connection has enough degrees of freedom to describe the classical gravitational and electromagnetic fields in the metric-affine formulation of gravity. The gravitational field is represented in the Lagrangian by the…
We study the energy-momentum pseudo-tensor of gravitational wave, and examine the one introduced by Landau-Lifshitz for a general gravitational field and the effective one recently used in literature. In short wavelength limit after…
One has not any conventional energy-momentum conservation law in Lagrangian field theory, but relations involving different stress-energy-momentum tensors associated with different connections. It is not obvious how to choose the true…
We generalize and simplify an earlier approach. In three dimensions we present the most general averaging formula in lowest order which respects the requirements of covariance. It involves a bitensor, made up of a basis of six tensors, and…
We consider a scalar-tensor theory of gravitation with the scalar source being the trace of the stress-energy tensor of the scalar field itself and matter. We obtain an example of a numerical solution of the cosmological equations which…
Based on a general variational principle, Noether's theorem is revisited. It is shown that the so called pseudotensor problem of the gravitational energy-momentum is a result of mis-reading Noether's theorem, and in fact, all the Noether's…
Multiple methods for deriving the energy-momentum tensor for a physical theory exist in the literature. The most common methods are to use Noether's first theorem with the 4-parameter Poincar\'{e} translation, or to write the action in a…
In this paper we show how a gravitational field generated by a given energy-momentum distribution (for all realistic cases) can be represented by distinct geometrical structures (Lorentzian, teleparallel and non null nonmetricity…
General relativity is the theory with unclear energy momentum tensor. An approach is considered, allowing to construct the energy momentum tensor for relativity with nonsymmetric metric. A consequence of the approach is confirmed in the…
In the context of a gauge theory for the translation group, a conserved energy-momentum gauge current for the gravitational field is obtained. It is a true spacetime and gauge tensor, and transforms covariantly under global Lorentz…
A theory of quantum gravity consists of a gravitational framework which, unlike general relativity, takes into account the quantum character of matter. In spite of impressive advances, no fully satisfactory, self-consistent and empirically…
We construct, and establish the (covariant) conservation of, a 4-index "super-stress tensor" for TMG. Separately, we discuss its invalidity in quadratic curvature models and suggest a generalization.
The total momentum of a thermodynamically closed system is unique, as is the total energy. Nevertheless, there is continuing confusion concerning the correct form of the momentum and the energy-momentum tensor for an electromagnetic field…
In Einstein's equation we suggest a geometrical object substituting the tensor of energy of impulse and tension. The obtained equation, together with the equation for external field, makes up the complete problem of mathematical equations…
We show that a three rank Lanczos type tensor field is an appropriate choice to describe relativistic electromagnetic and gravitational effects. More precisely, we identify the irreducible field-decompositions of this tensor as…
The usual derivation of Einstein's field equations from the Einstein--Hilbert action is performed by silently assuming the metric tensor's symmetric character. If this symmetry is not assumed, the result is a new theory, such as Einstein's…
The article describes a new approach to obtaining the energy-momentum tensor of electromagnetic field in medium without the use of Maxwell's equations and Poynting theorem. The energy-momentum tensor has new qualities and consequences. Its…
If the Einstein-Hilbert action ${\cal L}_{\rm EH}\propto R$ is re-expressed in Riemann-Cartan spacetime using the gauge fields of translations, the vierbein field $h^\alpha{}_\mu$, and the gauge field of local Lorentz transformations, the…
In General Relativity, there have been many proposals for defining the gravitational energy density, notably those proposed by Einstein, Tolman, Landau and Lifshitz, Papapetrou, M{\o}ller, and Weinberg. In this review, we firstly explored…