Related papers: Cyclic Szekeres Universes
Exact results stemming directly from Einstein equations imply that inhomogeneous Universes endowed with vanishing pressure density can only decelerate, unless the energy density of the Universe becomes negative. Recent proposals seem to…
The aim of this paper is to examine some obtained exact solutions of the Einstein-Maxwell equations, especially their properties from a chronological point of view. Each our spacetime is stationary cylindrically symmetric and it is filled…
The spectrum of known black-hole solutions to the stationary Einstein equations has been steadily increasing, sometimes in unexpected ways. In particular, it has turned out that not all black-hole-equilibrium configurations are…
Spherically symmetric, static model of the cosmological voids is constructed in the framework of the Tolman-Oppenheimer-Volkov equation with the cosmological constant. Extension of the Tooper result (dimensionless form of the TOV equation)…
This paper discusses an ordinary homogeneous differential equation of the second order with constant real-valued coefficients. The solution of this equation has to satisfy additional conditions. The first of the conditions stems from the…
We study static spherically symmetric solutions to Einstein's equations with a repulsive singularity at the centre. We show that geodesics are extendible across the singularity, so the singularity does not lead to pathological causality…
We analyze the evolution of cosmological perturbations in the cyclic model, paying particular attention to their behavior and interplay over multiple cycles. Our key results are: (1) galaxies and large scale structure present in one cycle…
Interior solutions of Einstein's equations with a non-zero cosmological constant are given for static and spherically symmetric configurations of uniform density. The metric tensor and pressure are determined for both positive and negative…
We present a singularity free class of inhomogeneous cylindrical universes filled with stiff perfect fluid $(\rho = p)$. Its matter free $ (\rho = 0)$ limit yield two distinct vacuum spacetimes which can be considered as analogues of Kasner…
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…
Several classic one-dimensional problems of variational calculus originating in non-relativistic particle mechanics have solutions that are analogues of spatially homogeneous and isotropic universes. They are ruled by an equation which is…
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…
A physicaly reasonable interpretation is provided for the perfect fluid, sphericaly symmetric, conformally flat ``Stephani Universes''. The free parameters of this class of exact solutions are determined so that the ideal gas relation $p=n…
We consider the possibility of describing the Higgs effect in unified theories without the Higgs potential in the presence of the Einstein gravity with the conformal gravity-scalar coupling under the assumption of homogeneous matter…
We introduce a two-parameter static, nonspherically-symmetric black hole solution in the Einstein theory of gravity coupled with a massless scalar field. The scalar field depends only on the polar coordinate $\theta$ in the spherical…
The exact general solution to the Einstein equations in a homogeneous Universe with a full causal viscous fluid source for the bulk viscosity index $m=1/2$ is found. We have investigated the asymptotic stability of Friedmann and de Sitter…
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…
The Schwarzschild solution is a complete solution of Einstein's field equations for a static spherically symmetric field. The Einstein's field equations solutions appear in the literature, but in different ways corresponding to different…
We analyze the stability of the Einstein static closed and open universe in two types of exponential $f(T)$ gravity theories. We show that the stable solutions exist in these two models. In particular, we find that large regions of…
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…