Related papers: Stationary Cylindrically Symmetric Solution Approa…
Previously the DeTurck 'trick' has been used to render the stationary Einstein's equation a well posed elliptic system that may be solved numerically by geometric flow or directly. Whilst in the static case for pure gravity with zero or…
A new family of exact solutions of the Einstein field equations for static and axially simmetric spacetimes is presented. All the metric functions of the solutions are explicitly computed and the obtained expressions are simply written in…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple star model: a self-gravitating perfect fluid ball with a differential rotation motion pattern. Using the…
We give a complete classification of all static, spherically symmetric solutions of the SU(2) Einstein-Yang-Mills theory with a positive cosmological constant. Our classification proceeds in two steps. We first extend solutions of the…
A scalar field generalization of Xanthopoulos's cylindrically symmetric solutions of the vacuum Einstein equation is obtained. The obtained solution preserves the properties of the Xanthopoulos solution, which are regular on the axis,…
Einstein's static model is the first relativistic cosmological model. The model is static, finite and of spherical spatial symmetry. I use the solution of Einstein's field equations in a homogeneous and isotropic universe -- Friedmann's…
In this talk we show a stiff fluid solution of the Einstein equations for a cylindrically symmetric spacetime. The main features of this metric are that it is non-separable in comoving coordinates for the congruence of the worldlineS of the…
We consider static spherically symmetric solutions of the Einstein equations with cosmological constant coupled to the SU(2) Yang Mills equations. We prove that most solutions can be continued back to the origin of spherical symmetry and…
Cylindrically symmetric inhomogeneous string cosmological models are investigated in presence of string fluid as a source of matter. To get the three types of exact solutions of Einstein's field equations we assume $A = f(x)k(t)$, $B =…
We consider static spherically symmetric solutions of Einstein's equations coupled to an SU(2) Yang Mills field that are smooth at the center of spherical symmetry. We prove that with small cosmological constant there exist solutions that…
As a first step in exploring time-periodic solutions of the Einstein equations with a negative cosmological constant, we study the cubic conformal wave equation on the Einstein cylinder. Using a combination of numerical and perturbative…
In this work we investigate analytic static and spherically symmetric solutions of a generalized theory of gravity in the Einstein-Cartan formalism. The main goal consists in analyzing the behavior of the solutions under the influence of a…
Perfect-fluid, static, cylindrically symmetric solutions of Einstein's field equations are obtained for the equations of state $\rho+3p=0$ and $\rho=p$. In the former case, the density and the pressure turn out to be constant while in the…
The general solution of the system of General Relativity equations has been found for isotropic Universe with the flat spatial distribution and synchronized time taking into account a perfect dust and the cosmological constant.…
It is proved that the only geodesically complete stationary vacuum solution of the Einstein equations is the empty Minkowski space, or a quotient of it by a discrete group of isometries, generalizing a classical result of Lichnerowicz. In…
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…
The non-linear superposition of the stationary euclidon solution with an arbitrary axially symmetric stationary gravitational field on the basis of the method of variation of parameters was constructed. Stationary soliton solution of the…
We construct an approximate solution to the cosmological perturbation theory around Einstein-de Sitter background up to the fourth-order perturbations. This could be done with the help of the specific symmetry condition imposed on the…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be considered as a simple star model: a self-gravitating perfect fluid ball with constant mass density rotating in rigid motion. Using…
We prove existence of static solutions to the cylindrically symmetric Einstein-Vlasov system, and we show that the matter cylinder has finite extension. The same results are also proved for a quite general class of equations of state for…