Related papers: On the Solutions of infinite systems of linear equ…
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…
We prove that the Einstein equations can be solved in a very general form for arbitrary spacetime dimensions and various types of vacuum and non-vacuum cases following a geometric method of anholonomic frame deformations for constructing…
A new class of higher-dimensional exact solutions of Einstein's vacuum equation is presented. These metrics are written in terms of the exponential of a symmetric matrix and when this matrix is diagonal the solution reduces to…
We consider static cosmological solutions along with their stability properties in the framework of a recently proposed theory of massive gravity. We show that the modifcation introduced in the cosmological equations leads to several new…
All Lorentz invariant solutions of vacuum Einstein's equations are found. It is proved that these solutions describe space-times of constant curvature.
The approach, referred to as "monodromy transform", provides some general base for solution of all known integrable space - time symmetry reductions of Einstein equations for the case of pure vacuum gravitational fields, in the presence of…
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…
An infinite family of relativistic finite thin disk model with magnetic field is presented. The model is obtained for solving the Einstein-Maxwell equations for static spacetimes by means of the Horsk\'y-Mitskievitch generating conjecture.…
A solution of the vacuum Einstein equations with a cosmological constant is exhibited which can perhaps be used to describe the interior of compact rotating objects, and may also provide a description of our universe on length scales…
In this paper, we construct several kinds of new time-periodic solutions of the vacuum Einstein's field equations whose Riemann curvature tensors vanish, keep finite or take the infinity at some points in these space-times, respectively.…
We present new criteria on the existence of fixed points that combine some monotonicity assumptions with the classical fixed point index theory. As an illustrative application, we use our theoretical results to prove the existence of…
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 system of singular integral equations with monotone and concave nonlinearity in the subcritical case is investigated. The specified system and its scalar analog have direct applications in various areas of physics and biology. In…
A solution of the Einstein vacuum field equations is constructed within the contex of perturbation theory. The solution possesses a graphical representation in terms of diagrams.
The existence of stationary solutions to the Einstein-Vlasov system which are axially symmetric and have non-zero total angular momentum is shown. This provides mathematical models for rotating, general relativistic and asymptotically flat…
The presence of a non-zero cosmological term in Einstein field equations can be interpreted as the physical possibility for preferred reference frames without breaking of general covariance. This possibility is used in the process of…
It is shown that, contrary to previous claims, a scalar tensor theory of Brans-Dicke type provides a relativistic generalization of Newtonian gravity in 2+1 dimensions. The theory is metric and test particles follow the space-time…
The construction of the general solution sequence of row-finite linear systems is accomplished by implementing -ad infinitum- the Gauss-Jordan algorithm under a rightmost pivot elimination strategy. The algorithm generates a basis (finite…
In this paper we construct a new kind of solutions of the Einstein's field equations with non-vanishing cosmological constant, which possess some interesting physical properties. The singularities of this kind of solutions are investigated.…
We show convexity of solutions to a class of convex variational problems in the Gauss and in the Wiener space. An important tool in the proof is a representation formula for integral functionals in this infinite dimensional setting, that…