Related papers: Linearized Einstein's field equations
We prove that given a solution of the Einstein equations $g_{ab}$ for the matter field $T_{ab}$, an autoparallel null vector field $l^{a}$ and a solution $(l_{a}l_{c}, \mathcal{T}_{ac})$ of the linearized Einstein equation on the given…
The cause of an infringement in GR of a gravitational field energy conservation law is investigated . The equation of a gravitational field not contradicting to the energy conservation law is suggested. This equation satisfy to the…
The analysis of a general multibody physical system governed by Einstein's equations in quite difficult, even if numerical methods (on a computer) are used. Some of the difficulties -- many coupled degrees of freedom, dynamic instability --…
Einstein's theory of gravity, General Relativity, has been precisely tested on Solar System scales, but the long-range nature of gravity is still poorly constrained. The nearby strong gravitational lens, ESO 325-G004, provides a laboratory…
We consider a brane-world of co-dimension one without the reflection symmetry that is commonly imposed between the two sides of the brane. Using the coordinate-free formalism of the Gauss-Codacci equations, we derive the effective Einstein…
We present a stationary spherically symmetric solution of the Einstein equations, with a source generated by a scalar field of $q$-theory. In this theory Riemannian gravity, as described by the Einstein - Hilbert action, is coupled to a…
In this paper, we are going to review the gravitating electromagnetic field in the 1+3 formalism on a general hyperbolic space-time manifold. We also discuss the recent results on the existence of the local field line solutions of the…
The similarities between linearized gravity and electromagnetism are known since the early days of General Relativity. Using an exact approach based on tidal tensors, we show that such analogy holds only on very special conditions and…
The Ernst formulation of the Einstein equations is generalised to accommodate $f(R)$ theories of gravity. It is shown that, as in general relativity, the axisymmetric $f(R)$ field equations for a vacuum spacetime that is either stationary…
This paper has been withdrawn by the author after further work showed the proposed theoretical approach cannot fit planetary perihelion precession data.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,…
In earlier work it was shown that a weak modification of general relativity, in the linearized approach, renders a spherically symmetric and stationary model of the Universe. This was due to the presence of a third mode of polarization in…
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…
In this paper Einstein's field equations, for static spherically symmetric perfect fluid models with a linear barotropic equation of state, are recast into a 3-dimensional regular system of ordinary differential equations on a compact state…
A simple general relativity theory for objects moving in gravitational fields is developed based on studying the behavior of an atom in a gravitational field. The theory is applied to calculate the satellite time dilation, light deflection…
We study a noncommutative deformation of general relativity where the gravitational field is described by a matrix-valued symmetric two-tensor field. The equations of motion are derived in the framework of this new theory by varying a…
Electron accelerations of the order of $10^{21} g$ obtained by laser fields open up the possibility of experimentally testing one of the cornerstones of general relativity, the weak equivalence principle, which states that the local effects…
We derive the Einstein field equations and black hole entropy from the first law of thermodynamics on a holographic time-like screen. Because of the universality of gravity, the stress tensor on the screen must be independent of the details…
A general affine connection has enough degrees of freedom to describe the classical gravitational and electromagnetic fields in the metric-affine formulation of gravity. The gravitational field is represented in the Lagrangian by the…
The gravitational field of a particle of small mass $\mu$ moving through curved spacetime, with metric $g_{ab}$, is naturally and easily decomposed into two parts each of which satisfies the perturbed Einstein equations through $O(\mu)$.…
Previous work has demonstrated that the gravitational field equations in all Lanczos-Lovelock models imply a thermodynamic identity TdS=dE+PdV (where the variations are interpreted as changes due to virtual displacement along the affine…