Related papers: Axially symmetric Einstein-Straus models
It is shown that a spacetime with collisionless matter evolving from data on a compact Cauchy surface with hyperbolic symmetry can be globally covered by compact hypersurfaces on which the mean curvature is constant and by compact…
Uniqueness of static, asymptotically flat, non-extremal {\it photon sphere} in Einstein-Maxwell spacetime with electric and magnetic charges has been proved. Using conformal positive energy theorem, as well as, the positive mass theorem and…
The purpose of this paper is to analyze the existence of static stable Einstein universe using inhomogeneous linear perturbations in the context of $f(R,T)$ gravity ($R$ and $T$ denote the scalar curvature and trace of the stress-energy…
We introduce a new type of generating theorems in General Relativity for anisotropic, static, spherically symmetric solutions of the Einstein field equations. The results are used to derive a class of solutions that can serve as new models…
The Einstein equations for a perfect fluid spatially homogeneous spacetime are studied in a unified manner by retaining the generality of certain parameters whose discrete values correspond to the various Bianchi types of spatial…
This paper studies the spatially homogeneous Einstein-de Sitter cosmological model in the context of a relativistic hierarchical (fractal) cosmology as developed in paper I (0807.0866). The Einstein-de Sitter model is treated as a special…
Recently, zero-point length cosmology has shown some positive insights into some non-singular aspects of the early Universe. In addition, topological defects are known to play a significant role by its presence as a part of the total energy…
When solving the equations of General Relativity in a symmetric sector, it is natural to consider the same symmetry for the geometry and stress-energy. This implies that for static and isotropic spacetimes, the most general natural…
We investigate the geodesic structure of realistic static and spherically symmetric spacetimes embedding neutron stars in metric $f(R)$ gravity, focusing on the quadratic Starobinsky model $f(R)=aR^2$ with $a<0$. Neutron-star solutions are…
The most general form of non-static plane symmetric space-times is considered to study proper curvature collineations by using the rank of the 6X6 Riemann matrix and direct integration techniques. Studying proper curvature collineations in…
The foundation of continuum elasticity theory is based on two general principles: (i) the force felt by a small volume element from its surrounding acts only through its surface (the Cauchy principle, justified by the fact that interactions…
Consider a rotating and possibly pulsating "star" in (2+1) dimensions. If the star is axially symmetric, then in the vacuum region surrounding the star, (a region that we assume at most contains a cosmological constant), the Einstein…
In many cases a scalar field can lead to accelerated expansion in cosmological models. This paper contains mathematical results on this subject particularly on type I Bianchi space-time. In this paper, global existence to the coupled…
The non-linear stability of the sub-extremal Schwarzschild-de Sitter spacetime in the stationary region near the conformal boundary is analysed using a technique based on the extended conformal Einstein field equations and a conformal…
It is useful to study the space of all cosmological models from a dynamical systems perspective, that is, by formulating the Einstein field equations as a dynamical system using appropriately normalized variables. We will discuss various…
We study locally spatially homogeneous solutions of the Einstein-Vlasov system with a positive cosmological constant. First the global existence of solutions of this system and the casual geodesic completeness are shown. Then the asymptotic…
Einstein's field equations for spatially self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are…
We present a new formulation of Einstein's equations for an axisymmetric spacetime with vanishing twist in vacuum. We propose a fully constrained scheme and use spherical polar coordinates. A general problem for this choice is the…
A new approach is suggested for the study of geometric symmetries in general relativity, leading to an invariant characterization of the evolutionary behaviour for a class of Spatially Homogeneous (SH) vacuum and orthogonal $\gamma -$law…
We showed that the principle of nongravitating vacuum energy, when formulated in the first order formalism, solves the cosmological constant problem. The most appealing formulation of the theory displays a local symmetry associated with the…