A better numerical solution stability by using the function developments in Cazacu's proper series.
A speculative approach to quantum gravity.
A stable class of spacetimes with naked singularities
We present a stable class of spacetimes which satisfy the conditions of the singularity theorem of Hawking & Penrose (1970), and which contain naked singularities. This offers counterexamples to a geometric version of the strong cosmic censorship hypothesis.
Algebro-geometric approach to the Ernst equation I. Mathematical Preliminaries
1. Introduction. It is well known that methods of algebraic geometry and, in particular, Riemann surface techniques are well suited for the solution of nonlinear integrable equations. For instance, for nonlinear evolution equations, so called 'finite gap' solutions have been found by the help of these methods. In 1989 Korotkin [9] succeeded in applying these techniques to the Ernst equation, which is equivalent to Einstein's vacuum equation for axisymmetric stationary fields. But, the Ernst equation...
An explicit determination of the space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle. Part III : Petrov type III space-times
An introduction to the Einstein-Vlasov system
Asymptotic completeness for the Klein-Gordon equation on the Schwarzschild metric
Blow-up for solutions of hyperbolic PDE and spacetime singularities
An important question in mathematical relativity theory is that of the nature of spacetime singularities. The equations of general relativity, the Einstein equations, are essentially hyperbolic in nature and the study of spacetime singularities is naturally related to blow-up phenomena for nonlinear hyperbolic systems. These connections are explained and recent progress in applying the theory of hyperbolic equations in this field is presented. A direction which has turned out to be fruitful is that...
Boundary conditions for the Einstein-Christoffel formulation of Einstein's equations.
Boundary value problems for the Vlasov-Maxwell system.
Complete solution of Hadamard's problem for the scalar wave equation on Petrov type III space-times
Complétude asymptotique pour l'équation des ondes dans une classe d'espaces-temps stationnaires et asymptotiquement plats
En utilisant une méthode dépendante du temps, nous démontrons la complétude asymptotique pour l'équation des ondes dans une classe d'espaces-temps stationnaires et asymptotiquement plats. On introduit l'observable de vitesse asymptotique et on décrit son spectre (sous des hypothèses plus faibles que pour la complétude asymptotique). Les méthodes utilisées sont inspirées par celles de l'analyse du problème à deux corps en mécanique quantique.
Consequences of the validity of Huygens' principle for the conformally invariant scalar wave equation, Weyl's neutrino equation and Maxwell's equations on Petrov type II space-times
Convergence of the 'relativistic' heat equation to the heat equation as c → ∞.
We prove that the entropy solutions of the so-called relativistic heat equation converge to solutions of the heat equation as the speed of light c tends to ∞ for any initial condition u0 ≥ 0 in L1(RN) ∩ L∞(RN).
Diffusion classique et quantique par un trou noir en formation
Dirac fields on asymptotically flat space-times [Book]
Existence of infinitely many distinct solutions to the quasirelativistic Hartree-Fock equations.
Formulazione intrinseca del problema di Cauchy in relatività generale
Viene stabilita una formulazione intrinseca del problema di Cauchy in Relatività generale, per uno spazio-tempo riemanniano descritto da un mezzo continuo globale e non-polare. In termini di variabili proprie: metrica, velocità angolare e di deformazione, densità di pura materia, flusso termico e temperatura. Vengono altresì precisate le condizioni iniziali per i dati di Cauchy su una assegnata superficie spaziale ; condizioni in involuzione nel senso d'E. Cartan, le quali mettono in evidenza,...
Generalized eigenfunctions of relativistic Schrödinger operators. I.
Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case