Related papers: The General Solution of Bianchi Type $VII_h$ Vacuu…
Bianchi VIII vacuum solutions to Einstein's equations are causally geodesically complete to the future, given an appropriate time orientation, and the objective of this article is to analyze the asymptotic behaviour of solutions in this…
We study the homogeneous and anisotropic evolution of Bianchi type-I spacetime driven by perfect fluid with shear viscosity. We obtain exact solutions by considering the simplest form of the equation of state wherein the pressure and the…
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…
It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. Numerical solutions for the anisotropic generalization of the Friedmann "flat" model $E^3$ for this…
We solve the local equivalence problem for second order (smooth or analytic) ordinary differential equations. We do so by presenting a {\em complete convergent normal form} for this class of ODEs. The normal form is optimal in the sense…
The necessary and sufficient conditions for a perfect fluid solution to define a spatially-homogeneous cosmology are achieved. These conditions are Intrinsic, Deductive, Explicit and ALgorithmic, and they offer an IDEAL labeling of these…
It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. Numerical solutions for the anisotropic generalization of the Friedmann "open" model $H^ 3$ for this…
A discrete symmetry of the four-dimensional string effective action is employed to derive spatially homogeneous and inhomogeneous string cosmologies from vacuum solutions of general relativity that admit two commuting spacelike Killing…
We report some new exact instantons in general relativity. These solutions are K\"ahler and fall into the symmetry classes of Bianchi types VI0 and VII0, with matter content of a stiff fluid. The qualitative behaviour of the solutions is…
In this paper, the crucial phenomenon of the expansion of the universe has been discussed. For this purpose, we study the vacuum solutions of Bianchi types $I$ and $V$ spacetimes in the framework of $f(R)$ gravity. In particular, we find…
Using dynamical systems theory and a detailed numerical analysis, the late-time behaviour of tilting perfect fluid Bianchi models of types IV and VII$_h$ are investigated. In particular, vacuum plane-wave spacetimes are studied and the…
In this paper, we examine the (LRS) Bianchi-type-I cosmological model with holographic dark energy. The exact solutions to the corresponding field equations are obtained by using generalized hybrid expansion law (HEL). The EoS parameter…
The dynamics and evolution of Bianchi type I space-times is considered in the framework of the four-dimensional truncation of a reduced theory obtained from the N=2,D=5 supergravity. The general solution of the gravitational field equations…
In the search for vacuum solutions, with or without a cosmological constant, of the Einstein field equations of Petrov type N with twisting principal null directions, the CR structures to describe the parameter space for a congruence of…
Einstein Gravitational Field Equations (EFE) of Chaplygin gas dominated Bianchi-type models are obtained by using metric approximation. The solutions of equations for a special case, namely Bianchi I model which is a generalization of…
The Einstein-Maxwell-dilaton field equations are considered for four-dimensional Bianchi type-V and VI$_0$ models. The general solutions have been obtained and their properties have been discussed.
We present the solution space of the field equations in the Einstein-aether theory for the case of a vacuum Bianchi Type V space-time. We also find that there are portions of the initial parameters space for which no solution is admitted by…
We consider the Bianchi I geometry coupled to several species of comoving barotropic perfect fluids with a linear equation of state in the context of general relativity. The solution of the dynamics can be reduced to a quadrature, which can…
The paper deals with the investigation of a homogeneous and anisotropic space-time described by Bianchi type III metric with perfect fluid in Lyra geometry setting. Exact solutions of the Einsten's field equations have been obtained under…
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…