Related papers: Exact Inhomogeneous Cosmological Models
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 general formula for the metric as an explicit function of the generic energy-momentum tensor is given which satisfies static plane symmetric Einstein's equations with cosmological constant.In order to illustrate it, the solutions for the…
In a previous work [I. Rodnianski and Y. Shlapentokh-Rothman, Naked Singularities for the Einstein Vacuum Equations: The Exterior Solution, arXiv:1912.08478] we constructed solutions to the Einstein vacuum equations in 3+1 dimensions which…
In this paper we investigate a class of solutions of Einstein equations for the plane-symmetric perfect fluid case with shear and vanishing acceleration. If these solutions have shear, they must necessarily be non-static. We examine the…
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…
In this lecture we will show some properties of a singularity-free solution to Einstein's equations and its accordance with some theorems dealing with singularities. We will also discuss the implications of the results.
We review some old and new results about strict and non strict hyperbolic formulations of the Einstein equations.
In this paper we derive homogeneous vacuum plane-wave solutions to Einstein's field equations in 4+1 dimensions. The solutions come in five different types of which three generalise the vacuum plane-wave solutions in 3+1 dimensions to the…
We present a new approach to find exact solutions for cosmological models. By requiring the existence of a symmetry transformation vector for the equations of motion of the given cosmological model (without using either Lagrangian or…
We investigate the dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations with Bianchi type I symmetry by using dynamical systems methods. All models are forever expanding and isotropize toward the future; toward the…
The Einstein field equations for a class of irrotational non-orthogonally transitive $G_{2}$ cosmologies are written down as a system of partial differential equations. The equilibrium points are self-similar and can be written as a…
We extend to the Einstein Maxwell Higgs system results first obtained previously in collaboration with V. Moncrief for Einstein equations in vacuum.
We find the general behaviour of homogeneous and isotropic cosmological models in some fourth-order theories of gravity. Explicit, exact, general solutions are given for both empty universes and those filled with a perfect fluid. For the…
We obtain an exact solution for the Einstein's equations with cosmological constant coupled to a scalar, static particle in static, "spherically" symmetric background in 2+1 dimensions.
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.
Einstein-Vlasov system is solved for a homogeneous isotropic spacetime with positive curvature. In the case of the Universe consisting of massless particles the equation for R(t) is solved analytically.
We review recent mathematical results concerning the high-frequency solutions to the Einstein vacuum equations and the limits of these solutions. In particular, we focus on two conjectures of Burnett, which attempt to give an exact…
Here we describe a stationary cylindrically symmetric solution of Einstein's equation with matter consisting of a positive cosmological and rotating dust term. The solution approaches Einstein static universe solution.
We derive the basic equations of the cosmological first-order post-Newtonian approximation from the recently formulated fully nonlinear and exact cosmological perturbation theory in Einstein's gravity. Apparently the latter, being exact,…
We have found new anisotropic vacuum solutions for the scale-invariant gravity theories which generalise Einstein's general relativity to a theory derived from the Lagrangian $R^{1+\delta}$. These solutions are expanding universes of Kasner…