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We study the plane-symmetric collision of two gravitational waves and describe the global spacetime geometry generated by this collision. To this end, we formulate the characteristic initial value problem for the Einstein equations, when…
A new family of nonlinear partial differential equations is presented. They represent a generalization of the hyperbolic Ernst equations for an Einstein-Mawxell-Weyl field in general relativity. A B\"acklund transformation for the system of…
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 generalise the electric-magnetic duality in standard Maxwell theory to its non-commutative version. Both space-space and space-time non-commutativity are necessary. The duality symmetry is then extended to a general class of…
The constraint equations in Maxwell theory are investigated. In analogy with some recent results on the constraints of general relativity it is shown, regardless of the signature and dimension of the ambient space, that the "divergence of a…
The theory of gauge transformations in linearized gravitation is investigated. After a brief discussion of the fundamentals of the kinetic theory in curved spacetime, the Einstein-Vlasov-Maxwell system of equations in terms of gauge…
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…
Interesting phenomena and problems arising from the coupling of large-scale electromagnetic fields and spacetime curvature, are introduced and studied within this thesis. From electromagnetic wave propagation in curved spacetime to…
Coupling the Maxwell tensor to the Riemann-Christoffel curvature tensor is shown to lead to a geometricized theory of electrodynamics. While this geometricized theory leads directly to the classical Maxwell equations, it also extends their…
In this paper, we have considered how to detect the processes of plane gravitational waves colliding. The degenerate Ferrari-Ibanez solution describes the collision of plane gravitational waves with aligned linear polarization, and the…
A planar superfluid is considered and interpreted in terms of electromagnetism and gravity. It has previously been suggested that the superfluid flow can be regarded as analogous to an electromagnetic field and that a non-vanishing density…
The energy content of (exact) electromagnetic and gravitational plane waves is studied in terms of super-energy tensors (the Bel, Bel-Robinson and the --less familiar-- Chevreton tensors) and natural observers. Starting from the case of…
An exact analytical model of the process of collision and nonlinear interaction of gravitational and/or electromagnetic soliton wave and strong non-soliton electromagnetic traveling wave of arbitrary profile propagating in the expanding…
Applying a simple harmonic map method to the cylindrically symmetric Einstein-Maxwell system, we obtain exact solutions representing strong nonlinear interaction between gravitational waves and electromagnetic waves in the case without any…
A quantization scheme for the phenomenological Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive and absorbing dielectric medium is developed. The classical Maxwell equations with spatially…
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…
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…
Fully non-linear, plane-symmetric exact solutions of the Einstein equations describing the scattering of gravitational and electromagnetic waves have existed for many years. For these closed-form solutions to be found, idealized wave…
We consider the interaction between gravitational and electromagnetic radiation propagating on a Minkowski background and look into the effects of the former upon the latter. Not surprisingly, the coupling between these two sources leads to…
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…