Related papers: The General Solution of Bianchi Type $VII_h$ Vacuu…
We construct numerical solutions to the higher-dimensional Einstein-Maxwell theory. The solutions are based on embedding the four dimensional Bianchi type IX space in the theory. We find the solutions as superposition of two functions,…
This manuscript investigate the dark energy Bianchi type-I cosmological models in presence of generalized Chaplygin gas, variable gravitational and cosmological constants. In this manuscript, exact solutions of Einstein field equations are…
In literature, it is known that any solution of Painlev\'{e} VI equation governs the isomonodromic deformation of a second order linear Fuchsian ODE on $\mathbb{CP}^{1}$. In this paper, we extend this isomonodromy theory on…
The subject of this article is the structure of big bang singularities in spatially homogeneous solutions to the Einstein non-linear scalar field equations. In particular, we focus on Bianchi class A; i.e., developments arising from left…
The problem of classification of exact solutions of Maxwell's vacuum equations for admissible electromagnetic fields and homogeneous space-time with the group of motions $G_3(VIII)$ according to the Bianchi classification is considered. All…
The second Bianchi identity can be recast as an evolution equation for the Riemann curvatures. Here we will report on such a system for a vacuum static spherically symmetric spacetime. This is the first of two papers. In the following paper…
In analogy with the standard derivation of the Schwarzschild solution, we find all static, cylindrically symmetric solutions of the Einstein field equations for vacuum. These include not only the well known cone solution, which is locally…
We analyze the dynamics of a class of cosmological solutions of the Einstein-Vlasov equations. These equations describe an ensemble of collisionless particles (which represent galaxies or clusters of galaxies) that interact gravitatively…
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…
The improved dynamics of loop quantum cosmology is extended to include the Bianchi type II model. Because these space-times admit both anisotropies and non-zero spatial curvature, certain technical difficulties arise over and above those…
A diagonal Bianchi Type III space-time is treated, both at the classical and quantum level, in the context of Horava - Lifshitz gravity. The system of the classical equations of motion is reduced to one independent Abel's equation of the…
Spatially homogeneous and anisotropic Bianchi type V space-time with bulk viscous fluid source and time varying gravitational constant $G$ and cosmological term $\Lambda$ are considered. Coefficient of bulk viscosity $\zeta$ is assumed as a…
We prove that a general class of nonlinear, non-autonomous ODEs in Fr\'echet spaces are close to ODEs in a specific normal form, where closeness means that solutions of the normal form ODE satisfy the original ODE up to a residual that…
New theorems about the existence of solution for a system of infinite linear equations with a Vandermonde type matrix of coefficients are proved. Some examples and applications of these results are shown. In particular, a kind of these…
According to Birkhoff's theorem the only spherically symmetric solution of the vacuum Einstein field equations is the Schwarzschild solution. Inspite of imposing asymptotically flatness and staticness as initial conditions we obtain that…
Some new exact solutions of Einstein's field equations in a spatially homogeneous and anisotropic Bianchi type-V space-time with minimally interaction of perfect fluid and dark energy components have been obtained. To prevail the…
A new class of time-symmetric solutions to the initial value constraints of vacuum General Relativity is introduced. These data are globally regular, asymptotically flat (with possibly several asymptotic ends) and in general have no…
In this paper, we investigate the energy problem in general relativity using approximate Lie symmetry methods for differential equations. This procedure is applied to Bardeen model (the regular black hole solution). Here we are forced to…
Einstein's field equations with variable gravitational and cosmological ``constant'' are considered in presence of perfect fluid for Bianchi type-I spacetime. Consequences of the four cases of the phenomenological decay of $\Lambda$ have…
Some new exact solutions of Einstein's field equations have come forth within the scope of a spatially homogeneous and anisotropic Bianchi type-III space-time filled with barotropic fluid and dark energy by considering a variable…