Related papers: Shear free solutions in General Relativity Theory
The symmetry method is used to derive solutions of Einstein's equations for fluid spheres using an isotropic metric and a velocity four vector that is non-comoving. Initially the Lie, classical approach is used to review and provide a…
We present new second derivative, generally covariant theories of gravity for spherically symmetric spacetimes (general covariance is in the $t-r$ plane) belonging to the class where the spherically symmetric Einstein-Hilbert theory is…
The Kerr-Schild double copy is a map between exact solutions of general relativity and Maxwell's theory, where the nonlinear nature of general relativity is circumvented by considering solutions in the Kerr-Schild form. In this paper, we…
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…
Although it is not a fundamental question, to determine exact and general solutions for a given theory has advantages over a numerical integration in many specific cases. Of course, respecting the peculiarities of the problem. Revisiting…
Several time dependent backgrounds, with perfect fluid matter, can be used to construct solutions of Einstein equations in the presence of a negative cosmological constant along with some matter sources. In this work we focus on the…
In order to find out whether empty singular boundaries can arise in higher dimensional Gravity, we study the solution of Einstein's equations consisting in a ($N+2$)-dimensional static and hyperplane symmetric perfect fluid satisfying the…
The Einstein theories of space-time and gravity as well the stander cosmology are reconstructed thoroughly in this paper based on flat reference frame. The rational parts of the Einstein theories are reserved while the irrational parts…
The qualitative properties of spatially homogeneous stiff perfect fluid and minimally coupled massless scalar field models within general relativity are discussed. Consequently, by exploiting the formal equivalence under conformal…
Recently, in a series of papers, we established the existence and found a general solution for the simultaneously rotating and twisting locally rotationally symmetric spacetimes in general relativity, which can model inhomogeneous and…
In the matrix model approaches of string/M theories, one starts from a generic symmetry $gl(\infty)$ to reproduce the space-time manifold. In this paper, we consider the generalization in which the space-time manifold emerges from a gauge…
We consider a system representing self-gravitating balls of dust in an expanding Universe. It is demonstrated that one can prescribe data for such a system at infinity and evolve it backward in time without the development of shocks or…
We discuss properties of conformal geodesics on general, vacuum, and warped product space-times and derive a system of conformal deviation equations. The results are used to show how to construct on the Schwarzschild-Kruskal space-time…
In Newtonian theory, gravity inside a constant density static sphere is independent of spacetime dimension. Interestingly this general result is also carried over to Einsteinian as well as higher order Einstein-Gauss-Bonnet (Lovelock)…
We study a rotating and expanding, Godel type metric, originally considered by Korotkii and Obukhov, showing that, in the limit of large times and nearby distances, it reduces to the open metric of Friedmann. In the epochs when radiation or…
The Einstein theories of space-time and gravity as well the stander cosmology are reconstructed thoroughly in this paper based on flat reference frame. The rational parts of the Einstein theories are reserved while the irrational parts…
We utilize a recent formulation of a spherically symmetric spacetime endowed with a general decomposition of the energy momentum tensor [Phys. Rev. D, 75, 024031 (2007)] to derive equations governing spherically symmetric distributions of…
Gravitational waves with parallel rays are known to have remarkable properties: Their orbit space of null rays possesses the structure of a non-relativistic spacetime of codimension-one. Their geodesics are in one-to-one correspondence with…
In this article, a cylindrical symmetry and static solution of the Einstein's field equations, was presented. The space-time is conformally flat, regular everywhere except on the symmetry axis where it possesses a naked curvature…
We develop sheaf-theoretic methods to deal with non-smooth objects in symplectic geometry. We show the completeness of a derived category of sheaves with respect to the interleaving distance and construct a sheaf quantization of a…