Related papers: Conserved non-Noether charge in general relativity…
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…
I exhibit the conflicting roles of Noether's two great theorems in defining conserved quantities, especially Energy in General Relativity and its extensions: It is the breaking of coordinate invariance through boundary conditions that…
This short report is dedicated to the 40th anniversary of International Journal of Modern Physics A (IJMPA) and Modern Physics Letters A (MPLA). While the report is based on a series of papers[1-8], its content reflects my personal…
This paper has three main aims: first, to give a pedagogical introduction to Noether's two theorems and their implications for energy conservation in general relativity, which was a central point of discussion between Hilbert, Klein,…
A covariant formula for conserved currents of energy, momentum and angular-momentum is derived from a general form of Noethers theorem applied directly to the Einstein-Hilbert action of classical general relativity. Energy conservation in a…
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…
In this paper, we investigate relations or differences among various conserved quantities which involve the matter Energy Momentum Tensor (EMT) in general relativity. These charges include the energy with Einstein's pseudo EMT, the…
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…
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…
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 present a precise definition of a conserved quantity from an arbitrary covariantly conserved current available in a general curved spacetime with Killing vectors. This definition enables us to define energy and momentum for matter by the…
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…
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…
The more precise definition and the more fundamental understanding of the concepts of time, energy, entropy and information are building upon the new, relativistic foundation of gravity. This lecture is an attempt to explain the basic…
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…
Noether's theorem identifies fundamental conserved quantities, called Noether charges, from a Hamiltonian. To-date Noether charges remain largely elusive within theories of gravity: We do not know how to directly measure them, and their…
Using the Noether Charge formulation, we study a perturbation of the conserved gravitating system. By requiring the boundary term in the variation of the Hamiltonian to depend only on the symplectic structure, we propose a general…
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…
Noether's theorem is reviewed with a particular focus on an intermediate step between global and local gauge and coordinate transformations, namely linear transformations. We rederive the well known result that global symmetry leads to…
Noether's 2nd theorem applied to a total system states that a global symmetry which is a part of local symmetries does not provide a physically meaningful conserved charge but it instead leads to off-shell constraints as a form of conserved…