A Hadamard type theorem for the space-time.
A model of gauge theory with invariant variables.
An introduction to the Einstein-Vlasov system
Analysis of a semi-Lagrangian method for the spherically symmetric Vlasov-Einstein system
We consider the spherically symmetric Vlasov-Einstein system in the case of asymptotically flat spacetimes. From the physical point of view this system of equations can model the formation of a spherical black hole by gravitational collapse or describe the evolution of galaxies and globular clusters. We present high-order numerical schemes based on semi-Lagrangian techniques. The convergence of the solution of the discretized problem to the exact solution is proven and high-order error estimates...
Around the bounded curvature conjecture in general relativity
We report on recent progress obtained on the construction and control of a parametrix to the homogeneous wave equation , where is a rough metric satisfying the Einstein vacuum equations. Controlling such a parametrix as well as its error term when one only assumes bounds on the curvature tensor of is a major step towards the proof of the bounded curvature conjecture.
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.
Cauchy data on a manifold
Characteristic evolution and matching.
Compact spacelike hypersurfaces with constant mean curvature in the anti de Sitter space.
Constraint-preserving boundary conditions for the linearized Baumgarte-Shapiro-Shibata-Nakamura formulation.
Duality-symmetric approach to general relativity and supergravity.
Einstein Metrics, Spinning Top Motions and Monopoles.
Event and apparent horizon finders for numerical relativity.
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,...
Gauge symmetries of an extended phase space for Yang-Mills and Dirac fields
Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case
Huygens' principle for the non-self-adjoint scalar wave equation on Petrov type III space-times
Hyperbolic methods for Einstein's equations.
Initial data for numerical relativity.