Résumé / Abstract Seminaire_GReCO

"Applications of the characteristic formalism in relativity"

Nigel Bishop
Department of Mathematics, Rhodes University (Grahamstown, Afrique du Sud)

In the characteristic formalism, coordinates are based on null cones generated by radially outgoing null geodesics. The Einstein equations take hierarchical form, and so can easily be written as a system suitable for numerical evolution. Further, the Einstein equations remain regular under radial compactification so that future null infinity can be included on a finite numerical grid. In numerical relativity, the major interest in the characteristic formalism is for Cauchy characteristic extraction, with the goal of extension to Cauchy characteristic matching.

In addition, there are other applications. Linearizing the Einstein equations about Minkowski leads to eigensolutions that take a remarkably simple (i.e., polynomial) form, and are used for testing numerical relativity codes and for the contsruction of characteristic initial data. Linearizing about Schwarzschild leads to eigensolutions that are more complicated, but which can be used to investigate quasi-normal modes, as well as the gravitational radiation produced by a particle orbiting a black hole.

Cosmology may be regarded as a characteristic problem, since nearly all cosmological data is a result of observations on our past null cone. It is in principle possible to measure the initial data required in order to calculate an evolution into the interior of the past null cone. Codes have been implemented to perform the evolution and have been tested against model data, because to date actual data is not complete enough to be used.

lundi 22 avril 2013 - 11:00
Salle Planck,
Institut d'Astrophysique de Paris

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