Related papers: General relativistic analogs of Poisson's equation…
The active mass density in Einstein's theory of gravitation in the analog of Poisson's equation in a local inertial system is proportional to $\rho+3p/c^2$. Here $\rho$ is the density of energy and $p$ its pressure for a perfect fluid. By…
After a historical introduction to Poisson's equation for Newtonian gravity, its analog for static gravitational fields in Einstein's theory is reviewed. It appears that the pressure contribution to the active mass density in Einstein's…
The Cartesian material space approach to Maxwell's equations reveals the analytical solution of the continuous radial density for the extended elementary charge. Radial charges and their Coulomb fields carry equal passive and active…
Gravitoelectromagnetic analogies are somewhat ubiquitous in General Relativity, and they are often used to explain peculiar effects of Einstein's theory of gravity in terms of familiar results from classical electromagnetism. Perhaps, the…
In the context of the teleparallel equivalent of general relativity, we show that the energy-momentum density for the gravitational field can be described by a true spacetime tensor. It is also invariant under local (gauge) translations of…
In a geometric unified theory there is an energy momentum equation, apart from the field equations and equations of motion. The general relativity Einstein equation with cosmological constant follows from this energy momentum equation for…
The lack of a well-established solution for the gravitational energy problem might be one of the reasons why a clear road to quantum gravity does not exist. In this paper, the gravitational energy is studied in detail with the help of the…
We first review the cosmological constant problem, and then mention a conjecture of Feynman according to which the general relativistic theory of gravity should be reformulated in such a way that energy does not couple to gravity. We point…
Starting with Newton's law of universal gravitation, we generalize it step-by-step to obtain Einstein's geometric theory of gravity. Newton's gravitational potential satisfies the Poisson equation. We relate the potential to a component of…
We show that Geroch decomposition leads us to Maxwell-like representation of gravity in $(3+1)$ metrics decomposition that may be perceived as Lorentz invariant version of GEM. For such decomposition we derive four-potential $V^\mu$ and…
We give a derivation of the Einstein equation for gravity which employs a definition of the local energy density of the gravitational field as a symmetric second rank tensor whose value for each observer gives the trace of the spatial part…
Linearized general relativity admits a formulation in terms of gravitoelectric and gravitomagnetic fields that closely parallels the description of the electromagnetic field by Maxwell's equations. For steady mass currents, this formalism…
The article proposes an amendment to the relativistic continuum mechanics which introduces the relationship between density tensors and the curvature of spacetime. The resulting formulation of a symmetric stress-energy tensor for a system…
By mass-energy equivalence, the gravitational field has a relativistic mass density proportional to its energy density. I seek to better understand this mass of the gravitational field by asking whether it plays three traditional roles of…
The averaging problem in general relativity is briefly discussed. A new setting of the problem as that of macroscopic description of gravitation is proposed. A covariant space-time averaging procedure is described. The structure of the…
The energy of gravitating systems has been an issue since Einstein proposed general relativity: considered to be ill defined, having no proper local density. Energy-momentum is now regarded as \emph{quasi-local} (associated with a closed…
We study gravitational properties of vacuum energy by erecting a geometry on the stress-energy tensor of vacuum, matter and radiation. Postulating that the gravitational effects of matter and radiation can be formulated by an appropriate…
We discuss the linear gravitoelectromagnetic approach used to solve Einstein equations in the weak-field and slow-motion approximation, which is a powerful tool to explain, by analogy with electromagnetism, several gravitational effects in…
We present a brief review of the teleparallel equivalent of general relativity and analyse the expression for the centre of mass density of the gravitational field. This expression has not been sufficiently discussed in the literature. One…
The presence of a non-zero cosmological term in Einstein field equations can be interpreted as the physical possibility for preferred reference frames without breaking of general covariance. This possibility is used in the process of…