Related papers: Consistency relations between the source terms in …
In a recent series of papers new exact analytical solutions of the Einstein equations representing interior spacetimes sourced by stationary rigidly rotating cylinders of different kinds of fluids have been displayed, [Phys. Rev. D {\bf…
We study the static cosmological solutions and their stability at background level in the framework of massive bigravity theory with Friedmann-Robertson-Walker (FRW) metrics. By the modification proposed in the cosmological equations…
We construct exact static inhomogeneous solutions to Einstein's equations with counter flow of particle fluid and a positive cosmological constant by using the Sasaki metrics on three-dimensional spaces. The solutions, which admit an…
A spherically symmetric charged ideal fluid solution of Einstein field equation is given in the presence of the cosmological constant and two well known example of this type of solution is presented. If the matter is confined in a region,…
We find the general behaviour of homogeneous and isotropic cosmological models in some fourth-order theories of gravity. Explicit, exact, general solutions are given for both empty universes and those filled with a perfect fluid. For the…
The theory of perfect fluids is reconsidered from the point of view of a covariant Lagrangian theory. It has been shown that the Euler-Lagrange equations for a perfect fluid could be found in spaces with affine connections and metrics from…
We review analytical solutions of the Einstein equations which are expressed in terms of elementary functions and describe Friedmann-Lema\^itre-Robertson-Walker universes sourced by multiple (real or effective) perfect fluids with constant…
It is shown that Einstein's field equations for \emph{all} perfect-fluid $k=0$ FLRW cosmologies have the same form as the topological normal form of a fold bifurcation. In particular, we assume that the cosmological constant is a…
In this work, we have obtained exact solutions of Einstein equations for static and axially symmetric magnetized matter, specifically in plane-symmetric and almost-plane symmetric cases. Although these solutions impose constraints on the…
In this talk r-form fields in spacetimes of any dimension D are considered (r<D). The weak-field Newtonian-type limit of Einstein's equations, in general, with relativistic sources is studied in the static case yielding a revision of the…
Axially symmetric stationary metrics governed by the Einstein-Euler equations for slowly rotating perfect fluids have been constructed in an arbitrarily large bounded domain containing the support of the mass density. However the problem of…
We show that for any perfect fluid in a static spacetime, if the Einstein constraint equation is satisfied and the temperature of the fluid obeys Tolman's law, then the other components of Einstein's equation are implied by the assumption…
We investigate the global dynamics of the field equations of (pure) quadratic theories of gravity which generalise Einstein's theory in spatially flat homogeneous and isotropic cosmological models with a perfect fluid. We introduce global…
Following a solution generating technique introduced recently by one of us, we transform the Einstein static Universe into a two - fold infinity class of physically acceptable exact perfect fluid solutions of Einstein's equations. Whereas…
The complete theory of cosmological evolution's macroscopic description is constructed with a help of self-consistent field. The theory includes a subsystem of linear equations of perturbations' evolution and nonlinear macroscopic Einstein…
We study Einstein's equations with an isotropic but inhomogeneous metric in the cosmic rest frame. The equations are solved perturbatively in the late Universe. The leading plus next-to-leading order results agree with observations without…
We examine the role of consistency with causality and quantum mechanics in determining the properties of gravitation. We begin by examining two different classes of interacting theories of massless spin 2 particles -- gravitons. One…
Examination of the Einstein energy-momentum relationship suggests that simple unbound forms of matter exist in a four-dimensional Euclidean space. Position, momentum, velocity, and other vector quantities can be expressed as Euclidean…
We provide exact solutions to the Einstein equations when the Universe contains vacuum energy plus a uniform arrangements of magnetic fields, strings, or domain walls. Such a universe has planar symmetry, i. e., it is homogeneous but, not…
A class of exact spherically symmetric perturbations of retarding automodel solutions linearized around Friedman background of Einstein equations for an ideal fluid with an arbitrary barotrope value is obtained and investigated.