Related papers: Mathematical Features of Several Cosmological Mode…
We consider the conformal Einstein equations for massless collisionless gas cosmologies which admit an isotropic singularity. It is shown that the Cauchy problem for these equations is well-posed with data consisting of the limiting…
An overview of some recent developments in inhomogeneous models is presented. As the volume and precision of cosmological data improves, it will become more and more essential to understand the non-linear behaviour of the Einstein field…
Higher dimensional solutions are obtained for a homogeneous, spatially isotropic cosmological model in Wesson theory of gravitation. Some cosmological parameter are also calculated for this model.
We construct exact static inhomogeneous solutions to Einstein's equations with counter flow of particle fluid and a positive cosmological constant by using the Sasaki metrics on three-dimensional spaces. The solutions, which admit an…
I give a compact, pedagogical review of our present understanding of the universe as based on general relativity. This includes the uniform models, with special reference to the cosmological 'constant'; and the equations for…
We show that the Einstein covariance principle provides an opportunity to generate infinitely many solutions of given covariant equation from a known one. With use of this statement we derive exact expressions for charge and current…
Much of the published work regarding the Isotropic Singularity is performed under the assumption that the matter source for the cosmological model is a barotropic perfect fluid, or even a perfect fluid with a $\gamma$-law equation of state.…
Gauge-invariant treatments of the second-order cosmological perturbation in a four dimensional homogeneous isotropic universe are formulated without any gauge fixing. We have derived the Einstein equations in the case of the single perfect…
The non-linearity of Einstein's equations makes it possible for small-scale matter inhomogeneities to affect the Universe at cosmological distances. We study the size of such effects using a simple heuristic model that captures the most…
Durgapal's fifth isotropic solution describing spherically symmetric and static matter distribution is extended to an anisotropic scenario. To do so we employ the gravitational decoupling through the minimal geometric deformation scheme.…
We obtain in terms of the Weierstrass elliptic $\wp-$function, sigma function, and zeta function an explicit parametrized solution of a particular nonlinear, ordinary differential equation. This equation includes, in special cases,…
Two distinct non-singular interior models that describe anisotropic spherical configurations are presented in this work. We develop the Einstein field equations and the associated mass function in accordance with a static spherical…
We discuss various space-time metrics which are compatible with Einstein's equations and a previously suggested cosmology with a finite total mass. In this alternative cosmology the matter density was postulated to be a spatial delta…
We construct new examples of complete Einstein metrics on balls. At each point of the boundary at infinity, the metric is asymptotic to a homogeneous Einstein metric on a solvable group, which varies with the point at infinity.
In this thesis we investigate cosmological models more general than the isotropic and homogeneous Friedmann-Lemaitre models. We focus on cosmologies with one spatial degree of freedom, whose matter content consists of a perfect fluid and…
We linearize the Einstein equations when the metric is Bondi-Sachs, when the background is Schwarzschild or Minkowski, and when there is a matter source in the form of a thin shell whose density varies with time and angular position. By…
In this paper I investigate the possibility to test Einstein's equations with observations of cosmological large scale structure. I first show that we have not tested the equations in observations concerning only the homogeneous and…
In this work numerical methods for solving Einstein's equations are developed and applied to the study of inhomogeneous cosmological models. A two-dimensional computer code is described which implements two advanced numerical methods:…
We use direct products of Einstein Metrics to construct new solutions to Einstein's Equations with cosmological constant. We illustrate the technique with three families of solutions having the geometries Kerr/de Sitter X de Sitter,…
The theory of cosmological perturbations is extended to spacetimes displaying isotropic expansion but anisotropic curvature. The perturbed Einstein equation and Boltzmann equations for massless and massive particles are derived in a general…