Karlsruhe 2011 – wissenschaftliches Programm

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GR: Fachverband Gravitation und Relativitätstheorie

GR 9: Hauptvorträge Donnerstag: Klassische Allgemeine Relativitätstheorie

GR 9.2: Hauptvortrag

Donnerstag, 31. März 2011, 14:45–15:30, 20.40: 101

The initial value problem of general relativity — •David Hilditch — Theoretical Physics Institute, University of Jena, 07743 Jena, Germany

I will give an overview of general relativity from the point of view of partial differential equations (PDEs). A crucial fact to establish about a given PDE system is whether or not it is well-posed, that is, whether or not unique solutions that depend continuously on given data exist. I will focus in particular on the gauge freedom of general relativity and the freedom it brings to the formulation of the initial value problem. Well-posedness of the initial value problem depends on whether or not the PDE system is in some sense wave-like. I will describe how the wave-like nature of gauge choices can be characterized, and how they may be coupled to the Einstein field equations. I will furthermore highlight the restriction that insisting on a Hamiltonian formulation brings to the system and the relationship between Hamiltonian structure and the PDE properties of the system. Finally I will consider the question: what are the set of gauge conditions that may be coupled to general relativity to form a wave-like PDE system?