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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.

Sasaki, Misao, Tagoshi, Hideyuki (2003)

Living Reviews in Relativity [electronic only]

Application of linear hyperbolic PDE to linear quantum fields in curved spacetimes : especially black holes, time machines and a new semi-local vacuum concept

Bernard Kay (2000)

Journées équations aux dérivées partielles

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.

Kaufmann, Ralph M., Livernet, Muriel, Penner, R. C. (2003)

Geometry & Topology

Around the bounded $L^{2}$ curvature conjecture in general relativity

Sergiu Klainerman, Igor Rodnianski, Jeremie Szeftel (2008)

Journées Équations aux dérivées partielles

We report on recent progress obtained on the construction and control of a parametrix to the homogeneous wave equation $□_{g} φ = 0$ , where $≫$ is a rough metric satisfying the Einstein vacuum equations. Controlling such a parametrix as well as its error term when one only assumes $L^{2}$ bounds on the curvature tensor $R$ of $≫$ is a major step towards the proof of the bounded $L^{2}$ curvature conjecture.

Asymptotic behavior of solutions to Schrödinger equations near an isolated singularity of the electromagnetic potential

Veronica Felli, Alberto Ferrero, Susanna Terracini (2011)

Journal of the European Mathematical Society

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.

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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

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

Arc operads and arc algebras.

Around the bounded $L^{2}$ curvature conjecture in general relativity

Asymptotic behavior of solutions to Schrödinger equations near an isolated singularity of the electromagnetic potential

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

Currently displaying 41 – 56 of 56