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We study the physical consequences of two diffferent but closely related perturbation schemes applied to the Einstein-Maxwell equations. In one case the starting space-time is flat while in the other case it is Schwarzschild. In both cases…
We consider Einstein-Maxwell-self-interacting scalar field theory described by a potential $V\left( \phi \right) $ in $2+1-$dimensions. The self-interaction potential is chosen to be a highly non-linear double-Liouville type. Exact…
This paper treats the time-harmonic electro-magnetic scattering or radiation problem governed by Maxwell's equations in an exterior weak Lipschitz domain divided into two disjoint weak Lipschitz parts We will present a solution theory using…
The main result of this paper is the proof that there are local electric and magnetic field configurations expressed in terms of field lines on an arbitrary hyperbolic manifold. This electromagnetic field is described by (dual) solutions of…
It is shown that there are three vacuum and one electrovacuum solutions of diagonal plane waves with M=0 and constant Maxwell scalars. Namely, these are the single wave, Stoyanov, Babala and Bell-Szekeres solutions. A comparison is made…
This paper introduces a new effort to study the collision of plane-fronted gravitational waves in four dimensional, asymptotically flat spacetime, using numerical solutions of the Einstein equations. The pure vacuum problem requires…
A benchmark problem for numerical relativity has been the head-on collision of two black holes starting from the ``Misner initial data,'' a closed form momentarily stationary solution to the constraint equations with an adjustable closeness…
We present three-dimensional simulations of Einstein equations implementing a symmetric hyperbolic system of equations with dynamical lapse. The numerical implementation makes use of techniques that guarantee linear numerical stability for…
We combine Maxwell's equations with Eulers's equation, related to a velocity field of an immaterial fluid, where the density of mass is replaced by a charge density. We come out with a differential system able to describe a relevant…
In this article, we are interested in the Einstein vacuum equations on a Lorentzian manifold displaying $\mathbb{U}(1)$ symmetry. We identify some freely prescribable initial data, solve the constraint equations and prove the existence of a…
We show that in four or more spacetime dimensions, the Einstein equations for gravitational perturbations of maximally symmetric vacuum black holes can be reduced to a single 2nd-order wave equation in a two-dimensional static spacetime for…
It is confirmed rigorously that the Killing-Cauchy horizons, which sometimes occur in space-times representing the collision and subsequent interaction of plane gravitational waves in a Minkowski background, are unstable with respect to…
Maxwell's vacuum equations are integrated for admissible electromagnetic fields in homogeneous spaces. Admissible electromagnetic fields are those for which the space group generates an algebra of symmetry operators ( integrals of motion )…
The complex form of Maxwell equations has been constructed as one equation for 3-dimensional complex A-vector. The real and imaginary parts of this vector are described with use of electric and magnetic tensions accordingly. With using a…
This paper explores ``black hole'' solutions of various Einstein-wave matter systems admitting an isometry of their domain of outer communications taking every point to its future. In the first two parts, it is shown that such solutions,…
We study the relationship between Lorentz harmonic maps into the hyperbolic plane and spacelike surfaces in anti-de Sitter 3-space. Using loop group techniques, we develop a DPW-type representation for Lorentz harmonic maps and provide an…
We study four-dimensional Einstein-Maxwell fields for which any higher-order corrections to the field equations effectively reduces to just a rescaling of the gravitational and the cosmological constant. These configurations are thus…
We consider the vector and the Lichnerowicz wave equations on the Schwarzschild spacetime, which correspond to the Maxwell and linearized Einstein equations in harmonic gauges (or, respectively, in Lorenz and de Donder gauges). After a…
Under the action of the Geroch group, the Minkowski metric can be transformed into any vacuum metric with two commuting Killing vectors. In principle, this reduces the problem of deriving vacuum metrics with two commuting Killing vectors to…
By using Bianchi I type of homogenous and anisotropic background metric having cylindrical symmetry in $x$ direction of a local cartesian coordinates system, we solve metric field equations for a non-minimally coupled Einstein-Maxwell…