Related papers: Finding and using exact solutions of the Einstein …
Einstein established the theory of general relativity and the corresponding field equation in 1915 and its vacuum solutions were obtained by Schwarzschild and Kerr for, respectively, static and rotating black holes, in 1916 and 1963,…
The Schwarzschild solution is a complete solution of Einstein's field equations for a static spherically symmetric field. The Einstein's field equations solutions appear in the literature, but in different ways corresponding to different…
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…
We study the cosmological evolution of the field equations in the context of Einstein-Aether cosmology by including a scalar field in a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker spacetime. Our analysis is separated into two…
This article is an overview of 100 years of testing general relativity, to be published in the book General Relativity and Gravitation: A Centennial Perspective, to commemorate the 100th anniversary of general relativity. It is effectively…
A new technique is presented for modifying the Einstein evolution equations off the constraint hypersurface. With this approach the evolution equations for the constraints can be specified freely. The equations of motion for the…
In this article we show that Einstein covariance principle provides a wide opportunity in the solutions of different problems of theoretical physics. Here we apply covariance principle in some problems of classical electrodynamics and…
The Einstein equations for static gravitational field depend on energy density and pressure. So one may expect that solutions should depend on two parameters: mass and its analogue originated from pressure. Yet the Schwarzschild solution…
In this thesis we consider several aspects of general relativity relating to exact solutions of the Einstein equations. In the first part gravitational plane waves in the Rosen form are investigated, and we develop a formalism for writing…
A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for…
The application of numerical relativity to cosmological spacetimes is providing new insights into the behavior of Einstein's equations, beyond common approximations. In order for simulations to be performed as accurately and efficiently as…
Some highlights of the priority in the discovery of the gravitational field equations are given.
For nearly a century, Einstein's theory of gravity has been the standard theory for describing gravitational phenomena in our universe. Along with its successes, limitations of the theory from theoretical (e.g., singularities) and…
The purpose of this article is to draw attention to some fundamental issues in General Relativity. It is argued that these deep issues cannot be resolved within the standard approach to general relativity that considers {\em every} solution…
We present a new formulation of Einstein's equations for an axisymmetric spacetime with vanishing twist in vacuum. We propose a fully constrained scheme and use spherical polar coordinates. A general problem for this choice is the…
Many numerical codes now under development to solve Einstein's equations of general relativity in 3+1 dimensional spacetimes employ the standard ADM form of the field equations. This form involves evolution equations for the raw spatial…
We introduce a proposal to modify Einstein's equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables of the modified system are essentially first integrals of the original constraints. The…
The ultimate application of Einstein's field equations is to empirically determine the geometry of the Universe from its matter content, rather than simply assuming the Universe can be represented by a homogeneous model on all scales.…
We find new classes of exact solutions to the Einstein-Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is…
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…