Related papers: A Generalized Representation Formula for Systems o…
The new formulation of the causal completion of spacetimes suggested in [1], and modified later in [2], is tested by computing the causal boundary for product spacetimes of a Lorentz interval and a Riemannian manifold. This is…
We establish a universal approach to solution of the word problem in the varieties of di- and tri-algebras. This approach, for example, allows to apply Groebner---Shirshov bases method for Lie algebras to solve the ideal membership problem…
If Einstein's equations are to describe a field theory of gravity in Minkowski spacetime, then causality requires that the effective curved metric must respect the flat background metric's null cone. The kinematical problem is solved using…
The general class of Robinson-Trautman metrics that describe gravitational radiation in the exterior of bounded sources in four space-time dimensions is shown to admit zero curvature formulation in terms of appropriately chosen…
A family of exact vacuum solutions, representing generalized plane waves propagating on the (anti-)de Sitter background, is constructed in the framework of Poincar\'e gauge theory. The wave dynamics is defined by the general Lagrangian that…
The Kerr-Schild-Kundt (KSK) metrics are known to be one of the universal metrics in general relativity, which means that they solve the vacuum field equations of any gravity theory constructed from the curvature tensor and its higher-order…
There has been proposed a new method of the constructing of the basic functions for spaces of tensor representations of the Lie groups with the help of the generalized Casimir operator. In the definition of the operator there were used the…
In this paper the asymmetric generalization of the Glazman-Povzner-Wienholtz theorem is proved for one-dimensional Schr\"{o}dinger operators with strongly singular matrix potentials from the space $H_{loc}^{-1}(\mathbb{R},…
In the sixties, DeWitt discovered that the advanced and retarded Green functions of the wave operator on metric perturbations in the de Donder gauge make it possible to define classical Poisson brackets on the space of functionals that are…
In this paper we have applied the generalized Kerr-Schild transformation finding a new family of stationary perfect-fluid solutions of the Einstein field equations. The procedure used combines some well-known techniques of null and timelike…
The Foldy-Wouthuysen transformation for relativistic spin-1 particles interacting with nonuniform electric and uniform magnetic fields is performed. The Hamilton operator in the Foldy-Wouthuysen representation is determined. It agrees with…
In this paper, we investigate the instability of one-dimensionally stable periodic traveling wave solutions of the generalized Korteweg-de Vries equation to long wavelength transverse perturbations in the generalized Zakharov-Kuznetsov…
We derive a general theorem relating the energy and momentum with the velocity of any solitary wave solution of the generalized KdV equation in $N$-dimensions that follows from an action principle. Further, we show that our $N$-dimensional…
A complete classification of the regular representations of the relations [T,X_j] = (i/k)X_j, j=1,...,d, is given. The quantisation of RxR^d canonically (in the sense of Weyl) associated with the universal representation of the above…
We introduce a natural generalization of the scattering equations, which connect the space of Mandelstam invariants to that of points on ${\mathbb{CP}^1}$, to higher-dimensional projective spaces $\mathbb{CP}^{k-1}$. The standard, $k=2$…
A detailed account is given on approximation schemes to the Einstein theory of general relativity where the iteration starts from the Newton theory of gravity. Two different coordinate conditions are used to represent the Einstein field…
We introduce a concept of causality in the framework of generalized pseudo-Riemannian Geometry in the sense of J.F. Colombeau and establish the inverse Cauchy-Schwarz inequality in this context. As an application, we prove a dominant energy…
The evolution equations of Einstein's theory and of Maxwell's theory---the latter used as a simple model to illustrate the former--- are written in gauge covariant first order symmetric hyperbolic form with only physically natural…
We prove a generalization of the classical Poincar\'e--Birkhoff theorem for Liouville domains, in arbitrary even dimensions. This is inspired by the existence of global hypersurfaces of section for the spatial case of the restricted…
A general covariant extension of Einstein\'{}s field equations is considered with a view to Numerical Relativity applications. The basic variables are taken to be the metric tensor and an additional four-vector $Z_\mu$. Einstein's solutions…