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The stability properties of the Einstein Static solution of General Relativity are altered when corrective terms arising from modification of the underlying gravitational theory appear in the cosmological equations. In this paper the…
In this paper, we describe the dynamics of a Bianchi Type V vacuum universe with an arbitrary cosmological constant. We begin by using an orthonormal frame approach to write Einstein's field equations as a coupled system of first-order…
We generalize the well-known Bonnor-Melvin solution of the Einstein-Maxwell equations to the case of a non-vanishing cosmological constant. The spacetime is again cylindrically symmetric and static but, unlike the original solution, it…
A new class of exact solutions of Einstein's field equations with bulk viscous fluid for an LRS Bianchi type-I spacetime is obtained by using deceleration parameter as variable. The value of Hubble's constant $H_{0}$ is found to be less…
A solution to the Einstein field equations that represents a rigidly rotating dust accompanied by a thin matter shell of the same type is found.
We derive the basic equations of the cosmological first-order post-Newtonian approximation from the recently formulated fully nonlinear and exact cosmological perturbation theory in Einstein's gravity. Apparently the latter, being exact,…
Recent results on solutions of the Einstein equations with matter are surveyed and a number of open questions are stated. The first group of results presented concern asymptotically flat spacetimes, both stationary and dynamical. Then there…
The staid subject of exact static spherically symmetric perfect fluid solutions of Einstein's equations has been reinvigorated in the last decade. We now have several solution generating techniques which give rise to new exact solutions.…
In this paper we study the Einstein-Boltzmann system for Israel particles with a positive cosmological constant. We consider spatially homogeneous solutions of Bianchi types except IX and obtain future global existence and asymptotic…
We derive explicit formulae for a set of constraints for the Einstein equations on a null hypersurface, in arbitrary dimensions. We solve these constraints and show that they provide necessary and sufficient conditions so that a spacetime…
Quantum geometrodynamics in extended phase space describes phenomenologically the integrated system ``a physical object + observation means (a gravitational vacuum condensate)''. The central place in this version of QGD belongs to the…
Brief account of results on the Cauchy problem for the Einstein equations starting with early the works of Darmois and Lichnerowicz and going up to the proofs of the existence and uniqueness of solutions global in space and local in time,…
We construct new classes of exact cosmological solutions to five dimensional Einstein-Maxwell-dilaton theory with two coupling constants for the dilaton-Maxwell term and dilaton-cosmological constant term. All the solutions are…
A general formula for the metric as an explicit function of the generic energy-momentum tensor is given which satisfies static plane symmetric Einstein's equations with cosmological constant.In order to illustrate it, the solutions for the…
We solve the one-dimensional boost-invariant kinetic equation for a relativistic massive system with the collision term treated in the relaxation time approximation. The result is an exact integral equation which can be solved numerically…
The issue of the cosmological constant is discussed in details and a solution to the problem is suggested.
In this paper we provide a method capable of producing an infinite number of solutions for Einstein's equation on static spacetimes with perfect fluid as a matter field. All spacetimes of this type which are symmetric with respect to a…
We introduce consideration of a new factor, synchronisation of spacetime Mixmaster oscillations, that may play a simplifying role in understanding the nature of the general inhomogeneous cosmological solution to Einstein's equations. We…
We show that small homogeneous solutions to the Einstein-Boltzmann-scalar field system exist globally towards the future and tend to the de Sitter solution in a suitable sense. More specifically, we assume that the spacetime is of Bianchi…
We construct two classes of exact solutions to six and higher dimensional Einstein-Maxwell theory in which the metric functions can be written as convolution-like integrals of two special functions. The solutions are regular everywhere and…