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A cosmological model describing the evolution of $n$ Einstein spaces $(n>1)$ with $m$-component perfect-fluid matter is considered. When all spaces are Ricci-flat and for any $\alpha$-th component the pressures in all spaces are…
We extend the monumental result of Christodoulou-Klainerman on the global nonlinear stability of the Minkowski spacetime to the global nonlinear stability of a class of large dispersive spacetimes. More precisely, we show that any regular…
Original abstract: "We construct periodic solutions of nonlinear wave equations using analytic continuation. The construction applies in particular to Einstein equations, leading to infinite-dimensional families of time-periodic solutions…
In this letter we construct a new time-periodic solution of the vacuum Einstein's field equations whose Riemann curvature norm takes the infinity at some points. We show that this solution is intrinsically time-periodic and describes a…
An infinite family of finite axisymmetric charged dust disks is presented. The disks are obtained by solving the Einstein-Maxwell equations for conformastatic spacetimes by assuming a functional dependency between the time-like component of…
The infinite cosmological "constant" limit of the de Sitter solutions to Einstein's equation is studied. The corresponding spacetime is a singular, four-dimensional cone-space, transitive under proper conformal transformations, which…
We construct infinite-dimensional families of non-singular static space times, solutions of the vacuum Einstein-Maxwell equations with a negative cosmological constant. The families include an infinite-dimensional family of solutions with…
Starting with a subclass of the four-dimensional spaces possessing two commuting Killing vectors and a non-trivial Killing tensor, we fully integrate Einstein's vacuum equation with a cosmological constant. Although most of the solutions…
Recent results of arXiv:1907.08788 on universal black holes in $d$ dimensions are summarized. These are static metrics with an isotropy-irreducible homogeneous base space which can be consistently employed to construct solutions to…
We find exact static solutions of the Einstein equations in the spacetime with plane symmetry, where an infinite slab with finite thickness and homogeneous energy (mass) density is present. In the first solution the pressure is isotropic,…
A formulation of Einstein's gravitational field equations in four space-time dimensions is presented using generalized differential forms and Cartan's equations for metric geometries. Cartan's structure equations are extended by using…
We prove that any 4-dimensional geodesically complete spacetime with a timelike Killing field satisfying the vacuum Einstein field equation $Ric(g_{M})=\lambda g_{M}$ with nonnegative cosmological constant $\lambda\geq 0$ is flat. When dim…
The Einstein Equation on 4-dimensional Lorentzian manifolds admitting recurrent null vector fields is discussed. Several examples of a special form are constructed. The holonomy algebras, Petrov types and the Lie algebras of Killing vector…
We study the solutions of the semiclassical Einstein equation in flat cosmological spacetimes driven by a massive conformally coupled scalar field. In particular, we show that it is possible to give initial conditions at finite time to get…
We present simulations of the Einstein-Maxwell-Klein-Gordon system on compactified hyperboloidal slices. To the best of our knowledge, this is the first time that this setup is evolved with a common formulation like BSSN/Z4. Hyperboloidal…
A new linear mapping of the linear vector space (LVS) of the octonions is suggested as an approach to the co-ordinatization of space-time. This approach resolves some perplexing issues concerning the validity of certain pre-metric notions…
We consider a characteristic initial value problem, with initial data given on a future null cone, for the Einstein (massless) scalar field system with a positive cosmological constant, in Bondi coordinates. We prove that, for small data,…
In this article, we construct explicit analytical exact solutions to the six and higher dimensional Einstein-Maxwell theory. In all solutions, a subspace of the metric is the Eguchi-Hanson space where the metric functions are completely…
In Einstein's equation we suggest a geometrical object substituting the tensor of energy of impulse and tension. The obtained equation, together with the equation for external field, makes up the complete problem of mathematical equations…
One of the possible applications of macroscopic Einstein equations has been considered. So, the nonsingular isotropic and uniform cosmological model is built. The cosmological consequences of this model are agree with conclusions of…