Seminar on

Mathematical General Relativity


 S. Klainerman (Princeton)

P.G. LeFloch (Paris)

A. Zeghib (Lyon)

Fondations des Sciences Mathématiques de Paris

ANR Project

“Mathematical General Relativity. Analysis and geometry of spacetimes with low regularity”

Thursday May 24, 2012

Laboratoire J-L Lions

Université Pierre et Marie Curie, Paris

Lecture room 15-25 104

11:00 am A. Shadi Tahvildar Zadeh (Rutgers) Zero-gravity limit of Kerr-Newman spacetimes and their electromagnetic fields

Abstract.  We discuss the limit of vanishing G (Newton’s constant of universal gravitation) of the Kerr–Newman electrovacuum spacetimes. We investigate the topologically nontrivial spacetime emerging in this limit and show that it consists of two copies of flat Minkowski spacetime glued at a timelike cylinder. The electromagnetic fields of the Kerr–Newman spacetimes converge to nontrivial solutions of Maxwell’s equations on this background spacetime. We show how to obtain these fields by solving Maxwell’s equations with singular sources supported only on a circle in a spacelike slice of the manifold. These sources do not suffer from any of the pathologies that plague the alternate sources found in previous attempts to interpret the Kerr–Newman fields on the topologically simple Minkowski spacetime.

2:00 pm James Isenberg (Eugene)  AVTD behavior in smooth solutions of Einstein’s equations

Abstract.  One of the more useful approaches to studying the Strong Cosmic Censorship conjecture in a family of solutions of Einstein’s equations is to first verify that generic solutions in that family exhibit AVTD (asymptotically velocity term dominated) behavior near their singular regions. It has been proven (by Ringstrom) that AVTD behavior occurs in generic Gowdy spacetimes, and it has also been shown that it occurs in at least some vacuum spacetimes with T2 isometry, and in some with U(1) isometry. These T2 and U(1) results have been proven using Fuchsian techniques, and have the unfortunate feature that, like many Fuchsian-based results, they require that the spacetimes be analytic. In work done with Florian Beyer, Philippe LeFloch, and Ellery Ames, we show that the analyticity condition can be removed, at least for the T2 case. To prove this result, we have developed a variant of the Fuchsian technique which does not require analyticity. It is very likely that this variant can be applied to U(1) symmetric vacuum spacetimes as well as to those with T2 symmetry.