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Stability of Minkowski space-time governed by the Einstein-Yang-Millsequations | Spectroscopy for asymmetric binary black hole mergers

来源: 04-28

时间:2024-04-29 Mon 15:30-17:00

地点:A3-4-101 ZOOM: 559 700 6085 BIMSA

组织者:Lars Andersson, Bowen Zhao

主讲人: Sari Ghanem BIMSA

Abstract

I shall start by presenting the Einstein-Yang-Mils system and by writing it in the Lorenz gaugeand in wave coordinates as a coupled system of non-linear hyperbolic partial differential equationsand l will then show how one constructs the initial data for a Cauchy hyperbolic formulation of theproblem, Thereafter, l will present the idea behind the proof of the non-inear stability of theMinkowski space-time, solution to the Einstein-Yang-Mills eguations, in the Lorenz gauge and inwave coordinates, in all space dimensions greater or equal to three, based on a continuityargument for a higher order weighted energy norm. in the critical case of three space-dimensions.we use a null frame decomposition, that was first used by Lindblad and Rodnianski for the Einsteinvacuum equations. We then deal with new difficulties that do not exist for Einstein vacuum nor forEinstein-Maxwell fields. In particular, we treat new terms that have a different structure in the non-linearities, and we derive a more refined formula to estimate the commutator temm. This provides anew independent proof of the result by Mondal and Yau, that l posted on arXiv in a series of threepapers that build up on each other, which cover all space dimensions greater or equal to three.

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