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Among the coordinates used to construct a conformal compactification of the Schwarzschild spacetime, none of them simultaneously extend smoothly both through an event horizon and beyond null infinity.To construct such coordinates, instead…
In this paper we prove the propagation of singularities for the wave equation on differential forms with natural (i.e. relative or absolute) boundary conditions on Lorentzian manifolds with corners, which in particular includes a…
We consider field localizing and concentration of electromagnetic waves governed by the time-harmonic anisotropic Maxwell system in a bounded domain. It is shown that there always exist certain boundary inputs which can generate…
The problem of unification of Gravitation and Electromagnetism in four dimensions; some new ideas involving mixtures of commuting and anti-commuting co-ordinates. Maxwell's equations are extracted in terms of the curvature of the…
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 study wave maps with values in S^d, defined on the future light cone {|x| <= t}, with prescribed data at the boundary {|x| = t}. Based on the work of Keel and Tao, we prove that the problem is well-posed for locally absolutely continuous…
We explore the impact of corrections to the propagation on the waveforms of gravitationally lensed gravitational waves under the geometrical optics approximation, focusing on both uniform cosmological modifications and local modifications…
We study, fully microlocally, the propagation of massive waves on the octagonal compactification \[\mathbb{O}=[\overline{\mathbb{R}^{1,d}};\mathscr{I};1/2]\] of asymptotically Minkowski spacetime, which allows a detailed analysis both at…
The existence of a scaling evolution for cosmic string loops in an expanding universe is demonstrated for the first time by means of numerical simulations. In contrast with what is usually assumed, this result does not rely on any…
This article begins with a brief introduction to numerical relativity aimed at readers who have a background in applied mathematics but not necessarily in general relativity. I then introduce and summarise my work on the problem of treating…
Current cosmological data indicate that our universe contains a substantial component of dark vacuum energy that is driving the cosmos to accelerate. We examine the immediate and longer term consequences of this dark energy (assumed here to…
We discuss the cosmology of axion-scalar systems in asymptotic limits of type IIB/F-theory flux compactifications. These results allow us to test a putative extension of the Distance Conjecture in a dynamical setting, which posits that…
Propagation of elastic waves along the axis of cylindrical shells is of great current interest due to their ubiquitous presence and technological importance. Geometric imperfections and spatial variations of properties are inevitable in…
We prove global existence for Einstein's equations with a charged scalar field for initial conditions sufficiently close to the Minkowski spacetime without matter. The proof relies on generalized wave coordinates adapted to the outgoing…
A systematic asymptotic expansion is developed for the gravitational wave degrees of freedom of a class of expanding, vacuum Gowdy cosmological spacetimes. In the wave map description of these models, the evolution of the gravitational wave…
A paradigm deeply rooted in modern numerical relativity calculations prescribes the removal of those regions of the computational domain where a physical singularity may develop. We here challenge this paradigm by performing…
In the first part of this article the various experimental sectors of physics in which Superluminal motions seem to appear are briefly mentioned, after a sketchy theoretical introduction. In particular, a panoramic view is presented of the…
A boundary integral equation formulation is presented for the electromagnetic transmission problem where an incident electromagnetic wave is scattered from a bounded dielectric object. The formulation provides unique solutions for all…
The geometric properties of spacetimes representing expanding impulsive gravitational waves, propagating on a flat background and generated by snapped cosmic strings, are studied. The construction of the line element is reviewed, and…
The scattering of electromagnetic waves by an obstacle is analyzed through a set of partial differential equations combining the Maxwell's model with the mechanics of fluids. Solitary type EM waves, having compact support, may easily be…