Related papers: Conserved non-Noether charge in general relativity…
The generalized Stokes theorem (connecting integrals of dimensions 3 and 4) is formulated in a curved space-time in terms of paths in Minkowski space (forming Path Group). A covariant integral form of the conservation law for the…
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…
We study various definitions of the gravitational field energy based on the usage of isometric embeddings in the Regge-Teitelboim approach. For the embedding theory we consider the coordinate translations on the surface as well as the…
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…
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…
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…
Thermodynamics plays an important role in gravitational theories. It is a principle independent of the gravitational dynamics, and there is still no rigorous proof to show that it is consistent with the dynamical principle. We consider a…
The generalized free energy landscape plays a pivotal role in understanding black hole thermodynamics and phase transitions. In general relativity, one can directly derive the generalized free energy from the contributions of black holes…
Towards the goal to quantize gravity, in this short review we discuss an intermediate step which consists in extending the picture of standard General Relativity by considering Extended Theories of Gravity. In this tapestry, the equations…
We propose a new formula for the entropy of a dynamical black hole$-$valid to leading order for perturbations off of a stationary black hole background$-$in an arbitrary classical diffeomorphism covariant Lagrangian theory of gravity in $n$…
A conserved current for generic quadratic curvature gravitational models is defined, and it is shown that, at the linearized level, it corresponds to the Deser-Tekin charges. An explicit expression for the charge for new massive gravity in…
We propose a geometrical treatment of symmetries in non-local field theories, where the non-locality is due to a lack of identification of field arguments in the action. We show that the existence of a symmetry of the action leads to a…
The parallel theory of relativity predicts conserved energy-momentum currents for an arbitrary metric, without invoking Killing symmetries. By treating the reference frame as an independent variational field and requiring it to carry no…
For Einstein's General Relativity (GR) or the alternatives suggested up to date the vacuum energy gravitates. We present a model where a new measure is introduced for integration of the total action in the D-dimensional space-time. This…
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.…
In Newtonian fluid dynamics simulations in which composition has been tracked by a nuclear reaction network, energy generation due to composition changes has generally been handled as a separate source term in the energy equation. A…
During the First World War, the status of energy conservation in general relativity was one of the most hotly debated questions surrounding Einstein's new theory of gravitation. His approach to this aspect of general relativity differed…
Gravity, and the puzzle regarding its energy, can be understood from a gauge theory perspective. Gravity, i.e., dynamical spacetime geometry, can be considered as a local gauge theory of the symmetry group of Minkowski spacetime: the…
The entropy of black holes in modified theories of gravity is examined in the Palatini formalism using the Noether Charge approach. It is shown that, if the gravitational coupling constant is properly identified, the entropy of a black hole…
We construct a relativistically covariant symmetry of QED. Previous local and nonlocal symmetries are special cases. This generalized symmetry need not be nilpotent, but nilpotency can be arranged with an auxiliary field and a certain…