A proof of strong cosmic censorship is presented for a class of solutions of the Einstein-Maxwell equations, those with polarized Gowdy symmetry. A key element of the argument is the observation that by means of a suitable choice of variables the central equations in this problem can be written in a form where they are identical to the central equations for general (i.e. non-polarized) vacuum G...

The aim of this paper is to review and classify the different methods that have been developed to enable stable long time simulations of the VlasovMaxwell equations and the Maxwell equations with sources. These methods can be classified in two types: field correction methods and sources correction methods. The field correction methods introduce new unknowns in the equations, for which additiona...

We study the system of self-dual Maxwell field coupled to 3D gravity with torsion, with Maxwell field modified by a topological mass term. General structure of the field equations reveals a new, dynamical role of the classical central charges, and gives a simple correspondence between self-dual solutions with torsion and their Riemannian counterparts. We construct two exact self-dual solutions,...

The behaviour of the Maxwell field near one of the spatial infinities of the Schwarzschild solution is analysed by means of the transport equations implied by the Maxwell equations on the cylinder at spatial infinity. Initial data for the Maxwell equations will be assumed to be expandable in terms of powers of a coordinate ρ measuring the geodesic distance to spatial infinity (in the conformal ...

In a previous work we examined the generalization of the Newman Tamburino metrics in the presence of an aligned Maxwell field [1]. It was shown there that the so called ‘spherical’ class did not admit any solutions and that consistency of the field equations therefore required the ‘cylindrical’ condition |ρ| = |σ|. The existence of solutions in the cylindrical class was left however as an open ...

The interpretation of the detection process in near-field optical microscopy is reviewed on the basis of a discussion about the possibility of establishing direct comparisons between experimental images and the solutions of Maxwell equations or the electromagnetic local density of states. On the basis of simple physical arguments, it is expected that the solutions of Maxwell equations should ag...

1 Introduction It is not uncommon to encounter the assertion that the dynamical evolution of the large-scale bulk velocity v of a collisionless gas is not described by the hydrodynamic (HD) equations. A favorite " reason " is the statement that pressure cannot be defined in the absence of collisions. Then in some quarters it is believed that the large-scale bulk dynamics of a swirling magnetize...