Related papers: Is energy conserved in general relativity ?
In General Relativity, finding out the geodesics of a given spacetime manifold is an important task because it determines which classical processes are dynamically forbidden. Conserved quantities play an important role in solving geodesic…
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…
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…
A new covariant generalization of Einstein's general relativity is developed which allows the existence of a term proportional to $T_{\alpha\beta}T^{\alpha\beta}$ in the action functional of the theory ($T_{\alpha\beta}$ is the…
We investigate the conservation law of energy-momentum in teleparallel gravity by using general Noether theorem. The energy-momentum current has also superpotential and is therefore identically conserved. The total energy-momentum, which…
We present a complete resolution of the Abraham-Minkowski controversy . This is done by considering several new aspects which invalidate previous discussions. We show that: 1)For polarized matter the center of mass theorem is no longer…
This work formulates and gives grounds for general principles and theorems that question the energy function doctrine and its quantum version as a genuine law of nature without borders of adequacy. The emphasis is on the domain where the…
Noether's first and second theorems both imply conserved currents that can be identified as an energy-momentum tensor (EMT). The first theorem identifies the EMT as the conserved current associated with global spacetime translations, while…
We calculate the relative conserved currents, superpotentials and conserved quantities between two homogeneous and isotropic universes. In particular we prove that their relative "energy" (defined as the conserved quantity associated to…
In certain modified theories of gravity, non-minimal couplings between matter and geometry lead to the nonconservation of the energy-momentum tensor. By interpreting this as an effective dissipative process, we formulate a general class of…
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…
If the presence of a gravitational field breaks the Lorentz symmetry valid for special relativity, an "absolute motion" might be detectable. We summarize a scalar theory of gravity with a such "ether", which starts from a tentative…
We present an introduction to mass and angular momentum in General Relativity. After briefly reviewing energy-momentum for matter fields, first in the flat Minkowski case (Special Relativity) and then in curved spacetimes with or without…
The most general expressions of the stored energies for time-harmonic electromagnetic fields are derived from the time-domain Poynting theorem, and are valuable in characterizing the energy storage and transport properties of complex media.…
The significance of past-pointing four-vectors and negative energies in general relativity is discussed. The sign of the energy is not absolute, but relative to the four-velocity of the observer, and every particle/observer always measures…
We investigate properties of the conserved charge in general relativity, recently proposed by one of the present authors with his collaborators, in the inflation era, the matter dominated era and the radiation dominated era of the expanding…
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…
This short note is concerned with the rotational invariance of the stored energy density in continuum physics as a scalar function of a few vectors. A simple derivation is presented for the determination of the general form of the energy…
In this article, we consider the Alcubierre spacetime, such a spacetime describes a ``bubble'' that propagates with arbitrary global velocity. This setting allows movement at a speed greater than that of light. There are some known problems…
It is shown that the familiar Larmor's formula or its relativistic generalization, Li\'enard's formula, widely believed to represent the instantaneous radiative losses from an accelerated charge, are not compatible with the special theory…