Related papers: Time-dependent Spherically-symmetric 5-D Vacuum So…
We investigate the interior Einstein's equations in the case of a static, axially symmetric, perfect fluid source. We present a particular line element that is specially suitable for the investigation of this type of interior gravitational…
We solve vacuum Einstein's field equations with the cosmological constant in space-times admitting 3-parameter group of isometries with 2-dimensional space-like orbits. The general exact solutions, which are represented in the advanced and…
Time-dependent analytic solutions of the Einstein-Skyrme system --gravitating Skyrmions--, with topological charge one are analyzed in detail. In particular, the question of whether these Skyrmions reach a spherically symmetric…
By an argument similar to that of Gibbons and Stewart, but in a different coordinate system and less restrictive gauge, we show that any weakly-asymptotically-simple, analytic vacuum or electrovacuum solutions of the Einstein equations…
Although cosmological solutions to Einstein's equations are known to be generically singular, little is known about the nature of singularities in typical spacetimes. It is shown here how the operator splitting used in a particular…
We study a time-dependent 5D metric which contains a static 4D sub-metric whose 3D part is spherically symmetric. An expansion in the metric coefficient allow us to obtain close-to Schwarzschild approximation to a class of…
Assuming that universe is the object of point rotation at a frequency, the relationship is established between this frequency and the cosmological constant. Using the transformation for point-like rotating coordinate systems, an unusual…
The static vacuum plane spacetimes are considered, which have two non-trivial solutions: The Taub solution and the Rindler solution. Imposed reflection symmetry, we find that the source for the Taub solution does not satisfy any energy…
In this paper we present Plane symmetric, Cylindrically Symmetric and Spherically Symmetric Black hole or Vacuum solutions of Einstein Field Equations(EFEs). Some of these solutions are new which we have not seen in the literature. This…
A new class of solutions to the coupled, spherically symmetric Einstein-Maxwell equations for a compact material source is constructed. Some of these solutions can be made to satisfy a number of requirements for being physically relevant,…
A closed expression for the harmonic oscillator wave function after the passage of a linear signal with arbitrary time dependence is derived. Transition probabilities are simple to express in terms of Laguerre polynomials. Spontaneous…
In this article we describe applications of the numerical method of discrete differential forms in computational GR. In particular we consider the initial value problem for vacuum space-times that admit plane gravitational waves. As…
Recent results on solutions of the Einstein equations with matter are surveyed and a number of open questions are stated. The first group of results presented concern asymptotically flat spacetimes, both stationary and dynamical. Then there…
Five classes of radiative solutions of Einstein's field equations are discussed in the light of some new developments. These are plane waves and their collisions, cylindrical waves, Robinson-Trautman and type N spacetimes, boost-rotation…
Harmonic coordinate conditions in stationary asymptotically flat spacetimes with matter sources have more than one solution. The solutions depend on the degree of smoothness of the metric and its first derivatives, which we wish to impose…
The paper is concerned with the Einstein equations for a spherically symmetric static distribution of anisotropic matter. The equations are cast into a system of Fuchsian type ODE for certain scalar invariants of the strain. And then the…
The topos theory is a theory which is used for deciding a number of problems of theory of relativity, gravitation and quantum physics. It is known that topos-theoretic geometry can be successfully developed within the framework of Synthetic…
This paper presents a systematical study of stationary (rotating) cylindrical space-times of a Weyl form that are solutions to D=4 Einstein-Maxwell equations with cosmological constant. The corresponding equations of motion - with zero…
When four-dimensional general relativity is embedded in an unconstrained man-ner in a fifth dimension, the physical quantities of spacetime can be interpreted as geometrical properties related to the extra dimension. It has become…
An exact solution of the Einstein field equations is found under the assumption of spherically symmetry and the existence of one-parameter group of homothetic motions. This solution has a singularity at $r = 0$, and has non-vanishing…