Related papers: General Relativity, Mental Causation, and Energy C…
In this paper, a modification of general relativity is considered. It consists of generalizing the Lagrangian of matter in a non-linear way, that is, replacing the curvature scalar $R$ by a function $f(R,T_{\mu\nu} T^{\mu\nu} )$, where…
An explicit proof of the vanishing of the covariant divergence of the energy-momentum tensor in modified theories of gravity is presented. The gravitational action is written in arbitrary dimensions and allowed to depend nonlinearly on the…
According to Yang \& Mills (1954), a {\it conserved} current and a related rigid (`global') symmetry lie at the foundations of gauge theory. When the rigid symmetry is extended to a {\it local} one, a so-called gauge symmetry, a new…
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…
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…
This paper has been withdrawn by the author after further work showed the proposed theoretical approach cannot fit planetary perihelion precession data. As presented, the theory doesn't fit gravitational light deflection by the sun either,…
Reflective equilibrium between physics and philosophy, and between GR and particle physics, is fruitful and rational. I consider the virtues of simplicity, conservatism, and conceptual coherence, along with perturbative expansions. There…
In the light of the local Lorentz transformations and the general Noether theorem, a new formulate of the general covariant angular momentum conservation law in Einstein-Cartan gravitation theory is obtained, which overcomes the critical…
In this work we revisit the study of the gravitational interaction in the context of the Special Theory of Relativity. It is found that, as long as the equivalence principle is respected, a relativistic non-linear energy conservation…
We explain the necessity of application of semi-metric in general relativity. A detailed discussion on the energy-momentum conservation in the general relativity is presented using the mathematical tool of semi-metric. By means of the…
Conservation laws have many applications in numerical relativity. However, it is not straightforward to define local conservation laws for general dynamic spacetimes due the lack of coordinate translation symmetries. In flat space, the rate…
In 1945 Einstein concluded that [1]: "The present theory of relativity is based on a division of physical reality into a metric field (gravitation) on the one hand, and into an electromagnetic field and matter on the other hand. In reality…
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…
We work out the most general theory for the interaction of spacetime geometry and matter fields -- commonly referred to as geometrodynamics -- for spin-$0$ and spin-$1$ particles. The minimum set of postulates to be introduced is that (i)…
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…
The problem of finding a covariant expression for the distribution and conservation of gravitational energy-momentum dates to the 1910s. A suitably covariant infinite-component localization is displayed, reflecting Bergmann's realization…
In this article, we will review Noether's Theorems and their application in General Relativity. We will present Noether's Theorems in their original form and restate them as they are usually applied to physics. Some basic equations of…
The Energy Problem (EP) in General Relativity (GR) is analyzed in the context of GR's axiomatic inconsistencies. EP is classified according to its local and global aspects. The local aspects of the EP include noncovariance of the…
General matterless--theories in 1+1 dimensions include dilaton gravity, Yang--Mills theory as well as non--Einsteinian gravity with dynamical torsion and higher power gravity, and even models of spherically symmetric d = 4 General…
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…