Related papers: Harmonic Map Formulation of Colliding Electrovac P…
An idea which has been around in general relativity for more than forty years is that in the approach to a big bang singularity solutions of the Einstein equations can be approximated by the Kasner map, which describes a succession of…
The purpose of the present work is to extend the earlier results for asymptotically flat vacuum space-times to asymptotically flat solutions of the Einstein-Maxwell equations. Once again, in this case, we get a class of asymptotically…
Colliding or noncolliding plane fronted electromagnetic or gravitational waves are the asymptotic limit of Robinson--Trautman spherical electromagnetic or gravitational waves. Noncolliding plane fronted waves contain no information about…
A formulation of Einstein equations is presented that could yield advantages in the study of collisions of binary compact objects during regimes between linear-nonlinear transitions. The key idea behind this formulation is a separation of…
In many numerical implementations of the Cauchy formulation of Einstein's field equations one encounters artificial boundaries which raises the issue of specifying boundary conditions. Such conditions have to be chosen carefully. In…
Explicit harmonic and wave maps are typically available only in highly symmetric or constant-curvature settings, where additional symmetry or integrability structures are present. We develop a reduction framework for pseudo-Riemannian…
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…
Some classes of the so called "travelling wave" solutions of Einstein and Einstein - Maxwell equations in General Relativity and of dynamical equations for massless bosonic fields in string gravity in four and higher dimensions are…
For space-times with two spacelike isometries, we present infinite hierarchies of exact solutions of the Einstein and Einstein--Maxwell equations as represented by their Ernst potentials. This hierarchy contains three arbitrary rational…
Integrable structures arise in general relativity when the spacetime possesses a pair of commuting Killing vectors admitting 2-spaces orthogonal to the group orbits. The physical interpretation of such spacetimes depends on the norm of the…
In this article we introduce a natural extension of the well-studied equation for harmonic maps between Riemannian manifolds by assuming that the target manifold is equipped with a connection that is metric but has non-vanishing torsion.…
For the plane symmetry we have found the electro-vacuum exact solutions of the Einstein-Maxwell equations and we have shown that one of them is equivalent to the McVittie solution of a charged infinite thin plane. The analytical extension…
In this paper the macroscopic Einstein and Maxwell equations for system, in which the electromagnetic interactions are dominating (for instance, the cosmological plasma before the moment of recombination), are derived. Ensemble averaging of…
We carry out a thorough analysis on a class of cosmological spacetimes which admit three space-like Killing vectors of Bianchi class B and contain electromagnetic fields. Using dynamical system analysis, we show that a family of vacuum…
The collision of two plane gravitational waves in Einstein's theory of relativity can be described mathematically by a Goursat problem for the hyperbolic Ernst equation in a triangular domain. We use the integrable structure of the Ernst…
Einstein-Maxwell theory implies the mixing of photons with gravitons in an external electromagnetic field. This process and its possible observable consequences have been studied at tree level for many years. We use the worldline formalism…
This article deals with the study of electromagnetic waves equations and the Lorentz condition, as emergent properties of Maxwell's system in the context of systems theory. To do this, the wave equations and the Helmholtz equation are first…
By gauging an Abelian electromagnetic (em) solution through a non-Abelian transformation and in accordance with a theorem proved long time ago, we construct a simple class of colliding Einstein-Yang-Mills (EYM) plane waves. The solution is…
Four-dimensional colliding plane wave (CPW) solutions have played an important role in understanding the classical non-linearities of Einstein's equations. In this note, we investigate CPW solutions in $2n+2$--dimensional Einstein gravity…
We show that the Maxwell equations describing an electromagnetic wave are a mathematical consequence of the Einstein equations for the same wave. This fact is significant for the problem of the Einsteinian metrics corresponding to the…