An explicit determination of the Petrov type N space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle
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 explicit determination of the space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle. — Part II : Petrov type D space-times
An introduction to the Einstein-Vlasov system
An operator equation and relativistic alterations in the time of radioactive decay.
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...
Analytic black hole perturbation approach to gravitational radiation.
Application of linear hyperbolic PDE to linear quantum fields in curved spacetimes : especially black holes, time machines and a new semi-local vacuum concept
Several situations of physical importance may be modelled by linear quantum fields propagating in fixed spacetime-dependent classical background fields. For example, the quantum Dirac field in a strong and/or time-dependent external electromagnetic field accounts for the creation of electron-positron pairs out of the vacuum. Also, the theory of linear quantum fields propagating on a given background curved spacetime is the appropriate framework for the derivation of black-hole evaporation (Hawking...
Arc operads and arc algebras.
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.
Asymptotic behavior of solutions to Schrödinger equations near an isolated singularity of the electromagnetic potential
Asymptotics of solutions to Schrödinger equations with singular magnetic and electric potentials is investigated. By using a Almgren type monotonicity formula, separation of variables, and an iterative Brezis–Kato type procedure, we describe the exact behavior near the singularity of solutions to linear and semilinear (critical and subcritical) elliptic equations with an inverse square electric potential and a singular magnetic potential with a homogeneity of order −1.
Asymptotic completeness for the Klein-Gordon equation on the Schwarzschild metric
Asymptotic waves and critical time in general relativistic magnetohydrodynamics
Averaging problem in general relativity and cosmology
Axiomatic approach to perturbative quantum field theory
Axiomatic foundations of the kinematics common to classical physics and special relativity
Basic Brane Mechanics
Black holes in higher dimensions.
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.