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Beginning with the self-dual two-forms approach to the Einstein equations, we show how, by choosing basis spinors which are proportional to solutions of the Dirac equation, we may rewrite the vacuum Einstein equations in terms of a set of…
The Newtonian approximation for the gravitational field equation should not necessarily involve admission of non-relativistic properties of the source terms in Einstein's equations: it is sufficient to merely consider the weak-field…
McVittie's spacetime is a spherically symmetric solution to Einstein's equation with an energy-momentum tensor of a perfect fluid. It describes the external field of a single quasi-isolated object with vanishing electric charge and angular…
In this letter we present the first multiparticle solutions to Einstein's field equations in the presence of matter. These solutions are iteratively obtained via the perturbiner method, which can circumvent gravity's infinite number of…
A solution to the gravitational field equations based on a non-symmetric metric tensor is examined. Unlike Einstein's interpretation of electromagnetism, or Moffat's generalized gravity, it is shown that the non-symmetric part of the metric…
A mathematical derivation of Maxwell's equations for gravitation, based on a mathematical proof of Faraday's Law, is presented. The theory provides a linear, relativistic Lagrangian field theory of gravity in a weak field, and paves the way…
A quantitative test for the validity of the semi-classical approximation in gravity is given. The criterion proposed is that solutions to the semi-classical Einstein equations should be stable to linearized perturbations, in the sense that…
We present time-dependent analytic solutions to the Einstein equations coupled with a dilaton (scalar) field. The background geometry for the solutions is a product of an N-dimensional spherically symmetric space and a d-dimensional flat…
We review the experimental evidence for Einstein's special and general relativity. A variety of high precision null experiments verify the weak equivalence principle and local Lorentz invariance, while gravitational redshift and other clock…
It is a known fact that the Kerr-Schild type solutions in general relativity satisfy both exact and linearized Einstein field equations. We show that this property remains valid also for a special class of the Kerr-Schild metrics in…
The Einstein-$\AE$ther theory has drawn a lot of attentions in recent years. As a representative case of gravitational theories that break the Lorentz symmetry, it plays an important role in testing the Lorentz-violating effects and…
We show that Einstein's $R^{\hat{0} \hat{0}}$ equation for nonrelativistic matter and strong gravitational fields is identical with Newton's equation for relative radial acceleration of neighbouring freefalling particles, spherically…
We construct a class of Einstein-vector theories where the vector field couples bilinearly to the curvature polynomials of arbitrary order in such a way that only Riemann tensor rather than its derivative enters the equations of motion. The…
For conformally K\"ahler Riemannian four-manifolds with a Killing field, we present a framework to solve the field equations for generalised gravitational instantons corresponding to conformal self-duality and to cosmological…
We study the three dimensional Einstein gravity conformally coupled to a scalar field. Solutions of this theory are geometries with vanishing scalar curvature. We consider solutions with a constant scalar field which corresponds to an…
This paper is devoted to investigate the exact solutions of Bianchi types I and V spacetimes in the context of f(R, T) gravity [1]. For this purpose, we found two exact solutions in each case by using assumption of constant deceleration…
We give an alternative description of the physical content of general relativity that does not require a Lorentz invariant spacetime. Instead, we find that gravity admits a dual description in terms of a theory where local size is…
A non-geometrical (but with curved space) theory of gravitation characterized by a vector field representing gravitational matter and a metric tensor presenting space is presented. It is derived from a more general theory of matter and…
We investigate gravitational properties of thin planar wall solutions of the Einstein's equations in the weak field approximation. We find the general metric solutions and discuss the behavior of a particle placed initially at rest to one…
With the arrival of the era of gravitational wave astronomy, the strong gravitational field regime will be explored soon in various aspects. In this article, we provide a general review over cylindrical systems in Einstein's theory of…