Related papers: Solution generating methods as "coordinate" transf…
It is formulated a new 'anholonomic frame' method of constructing exact solutions of Einstein equations with off--diagonal metrics in 4D and 5D gravity. The previous approaches and results are summarized and generalized as three theorems…
It is shown how to generate three-dimensional Einstein-Maxwell fields from known ones in the presence of a hypersurface-orthogonal non-null Killing vector field. The continuous symmetry group is isomorphic to the Heisenberg group including…
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…
There are many complementary approaches to the construction of solutions to the field equations of general relativity. Among these, numerical approximation offers the only possibility to compute a variety of dynamical spacetimes, and so has…
A new formalism for construction of the stationary solutions is developed for the four-dimensional gravity coupled to the dilaton, Kalb-Ramond and two Maxwell fields in a low-energy heterotic string theory form. The result of generation is…
Singular solutions of the harmonic Einstein evolution equation are constructed which are related to spatially global and time-local solutions for a certain class of quasilinear hyperbolic systems of second order. The constructed…
This work is devoted to systematically study general $N$-soliton solutions possibly containing multiple degenerate soliton groups (DSGs), in the context of the sharp-line Maxwell-Bloch equations with a zero background.We also show that…
A unified general approach is presented for construction of solutions of the characteristic initial value problems for various integrable hyperbolic reductions of Einstein's equations for space-times with two commuting isometries in General…
A systematic study of deformations of four-dimensional Einsteinian space-times embedded in a pseudo-Euclidean space $E^N$ of higher dimension is presented. Infinitesimal deformations, seen as vector fields in $E^N$, can be divided in two…
We report a new family of solutions to Einstein-Maxwell-dilaton gravity in 2+1 dimensions and Einstein-Maxwell gravity with cylindrical symmetry in 3+1 dimensions. A set of static charged solutions in 2+1 dimensions are obtained by a…
We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We…
A nonlinear charged version of the (2+1)-anti de Sitter black hole solution is derived. The source to the Einstein equations is a Born-Infeld electromagnetic field, which in the weak field limit becomes the (2+1)-Maxwell field. The obtained…
An explicit one-parameter Lie point symmetry of the four-dimensional vacuum Einstein equations with two commuting hypersurface-orthogonal Killing vector fields is presented. The parameter takes values over all of the real line and the…
We consider three methods by which one can generate new cosmological models. Two of these are based on the Lorentzian structure of spacetime. In a Lorentzian manifold there can exist horizons that separate regions of spacetime that can be…
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…
We numerically investigate the dynamics near black hole formation of solutions to the Einstein--Vlasov system in axisymmetry. Our results are obtained using a particle-in-cell and finite difference code based on the $(2+1)+1$ formulation of…
Several types of static solutions to Einstein's equations coupled with antisymmetric tensor fields are found in $(2+N+1)$-dimensional spacetime. The solutions describe a product of a three-dimensional radially symmetric spacetime and an…
We develop solution-generating techniques for stationary metrics with one angular momentum and axial symmetry, in the presence of a cosmological constant and in arbitrary spacetime dimension. In parallel we study the related lower…
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 describe a grid generation procedure designed to construct new classes of orthogonal coordinate systems for binary black hole spacetimes. The computed coordinates offer an alternative approach to current methods, in addition to providing…