Related papers: Time-Periodic Solutions of the Einstein's Field Eq…
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…
We show that there is a phenomenologically and theoretically consistent limit of the generic Einstein-Aether theory in which the Einstein-Aether field equations reduce to Einstein field equations with a perfect fluid distribution sourced by…
A new solution of the Einstein-Born-Infeld theory in 2+1 space-time is derived. A new solution has no horizon there are two singularity. This space-time has two singular points, however, one of the point at the origin is not in the physical…
In this paper, we study one-dimensional nonhomogeneous isentropic compressible Euler equations with time-periodic boundary conditions. With the aid of the energy methods, we prove the existence and uniqueness of the time-periodic supersonic…
This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local in time Cauchy problem, which is relatively well understood, is…
We consider plane-symmetric spacetimes satisfying Einstein's field equations with positive cosmological constant, when the matter is a fluid whose pressure is equal to its mass-energy density (i.e. a so-called stiff fluid). We study the…
In Einstein's general relativity, with its nonlinear field equations, the discoveries and analyzes of various specific explicit solutions made a great impact on understanding many of the unforeseen features of the theory. Some solutions…
This paper develops a method for solving Einstein's equation numerically on multi-cube representations of manifolds with arbitrary spatial topologies. This method is designed to provide a set of flexible, easy to use computational…
We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills…
We apply thermodynamics method to generate exact solution with maximum symmetric surface for Einstein equation without solving it. The exact solutions are identified with which people have solved before. The horizons structure of solutions…
In this paper, we present a framework for getting a series of exact vacuum solutions to the Einstein equation. This procedure of resolution is based on a canonical form of the metric. According to this procedure, the Einstein equation can…
We review analytical solutions of the Einstein equations which are expressed in terms of elementary functions and describe Friedmann-Lema\^itre-Robertson-Walker universes sourced by multiple (real or effective) perfect fluids with constant…
We present a simple method to obtain vacuum solutions of Einstein's equations in parabolic coordinates starting from ones with cylindrical symmetries. Furthermore, a generalization of the method to a more general situation is given together…
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 general exact solution of the Einstein-matter field equations describing spherically symmetric shells satisfying an equation of state in closed form is discussed under general assumptions of physical reasonableness. The solutions split…
We study the dynamics of two-component Bose-Einstein condensates in periodic potentials in one dimension. Elliptic potentials which have the sinusoidal optical potential as a special case are considered. We construct exact nonstationary…
Within a semiclassical framework, we investigate spherically symmetric solutions of the Einstein equations that (i) develop a trapped region within a finite time as measured by distant observers, and (ii) remain sufficiently regular at the…
A new class of spacetime defect solutions of Einstein Field equations of Edelen's direct Poincar\'{e} Gauge Field theory without biaxial symmetry is presented. The interior solution describes a core of defects where curvature vanishes and…
We consider static cosmological solutions along with their stability properties in the framework of a recently proposed theory of massive gravity. We show that the modifcation introduced in the cosmological equations leads to several new…
Rigorous results on solutions of the Einstein-Vlasov system are surveyed. After an introduction to this system of equations and the reasons for studying it, a general discussion of various classes of solutions is given. The emphasis is on…