Freiburg 2008 – wissenschaftliches Programm

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GR: Fachverband Gravitation und Relativitätstheorie

GR 10: Hauptvorträge Donnerstag

GR 10.2: Hauptvortrag

Donnerstag, 6. März 2008, 09:00–09:45, KGI-HS 1010

An isoperimetric concept for mass and energy of isolated systems — •Gerhard Huisken — Albert-Einstein-Institut, Am Mühlenberg 1, 14476 Golm

It is a basic problem of General Relativity to represent physical concepts like mass, center of mass, momentum or angular momentum of isolated gravitating systems by natural geometric structures in order to ensure invariance of these concepts under coordinate changes. The lecture explains how a 4-dimensional spacetime representing an isolated gravitating system can be decomposed in a narural way into 3-dimensional timeslices carrying 2-dimensional radial foliations that allow geometric definitions for mass and momentum. It is shown how the "total mass" of the system can then be interpreted in terms of the classical isoperimetric inequality relating volume and perimeter of regions in the 3-dimensional timeslice. The lecture also discusses how methods from geometric analysis justify these concepts and imply sharp lower bounds such as the Penrose inequality on the energy systems containing black holes.