Related papers: Oscillatory singularities in Bianchi models with m…
The dynamics of the Einstein-Vlasov equations for a class of cosmological models with four Killing vectors is discussed in the case of massive particles. It is shown that in all models analysed the solutions with massive particles are…
We consider spherically symmetric Einstein-massless-scalar field equations with negative cosmological constant in five dimensions and analyze evolution of small perturbations of anti-de Sitter spacetime using the recently proposed resonant…
General relativity probably is not the definitive theory of gravity, due a number or issues, both from the theoretical and from the observational point of view. Alternative theories of gravity were conceived to extend general relativity and…
In classical general relativity, the generic approach to the initial singularity is usually understood in terms of the BKL scenario. In this scenario, along with the Bianchi IX model, the exact, singular, Kasner solution of vacuum Bianchi I…
Self-consistent system of spinor, scalar and BI gravitational fields is considered. Exact solutions to the field equations in terms of volume scale of the BI metric are obtained. Einstein field equations in account of the cosmological…
The fundamental metrics, which describe any static three-dimensional Einstein-Maxwell spacetime (depending only on a unique spacelike coordinate), are found. In this case there are only three independent components of the electromagnetic…
The Einstein equations are non-linear and the particles of which the gravitational effect is described by these equations are lastly unknown. If renormalizable fields are assumed, then results are obtained only in the case of a at space.…
This article is the second of two in which we develop a geometric framework for analysing silent and anisotropic big bang singularities. In the present article, we record geometric conclusions obtained by combining the geometric framework…
As shown in the classic work of Belinski, Khalatnikov and Lifshitz, the approach to a generic space-like singularity in general relativity consists of a sequence of eras and epochs in which the metric is locally Kasner, connected by brief…
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 consider the Cauchy problem of 2+1 equivariant wave maps coupled to Einstein's equations of general relativity and prove that two separate (nonlinear) subclasses of the system disperse to their corresponding linearized equations in the…
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…
Motivated by the structure of one-loop vacuum polarization effects in curved spacetime we discuss a non-minimal extension of the Einstein-Maxwell equations. This formalism is applied to Bianchi I models with magnetic field. We obtain…
The vacuum cosmological model on the manifold $R \times M_1 \times \ldots \times M_n$ describing the evolution of $n$ Einstein spaces of non-zero curvatures is considered. For $n = 2$ the Einstein equations are reduced to the Abel (ordinary…
In axial symmetry, there is a gauge for Einstein equations such that the total mass of the spacetime can be written as a conserved, positive definite, integral on the spacelike slices. This property is expected to play an important role in…
We investigate the Einstein equation with a positive cosmological constant for $4n+4$-dimensional metrics on bundles over Quaternionic K\"ahler base manifolds whose fibers are 4-dimensional Bianchi IX manifolds. The Einstein equations are…
The Einstein-Maxwell equations in D-dimensions admitting (D-3) commuting Killing vector fields have been investigated. The existence of the electric, magnetic and twist potentials have been proved. The system is formulated as the harmonic…
We analyze the global dynamics of Bianchi type I solutions of the Einstein equations with anisotropic matter. The matter model is not specified explicitly but only through a set of mild and physically motivated assumptions; thereby our…
The evolution of the methods used to find solutions of Einstein's field equations during the last 100 years is described. Early papers used assumptions on the coordinate forms of the metrics. Since the 1950s more invariant methods have been…
The emergent mechanism provides a possible way to resolve the big bang singularity problem by assuming that our universe originates from the Einstein static (ES) state. Thus, the existence of a stable ES solution becomes a very crucial…