Göttingen 2012 – scientific programme

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GR: Fachverband Gravitation und Relativitätstheorie

GR 4: Klassische Allgemeine Relativitätstheorie

GR 4.2: Talk

Monday, February 27, 2012, 18:00–18:20, ZHG 002

Cartan geometrodynamics — •Derek Wise — Institut für Theoretische Physik III, Uni. Erlangen-Nürnberg, Staudtstr. 7/B2, 91058 Erlangen, Germany

The MacDowell-Mansouri formulation of gravity is based on broken de Sitter symmetry. Geometrically, this is best understood in terms of Cartan geometry, in which breaking symmetry from a group G to a group H plays the role of describing geometry relative to the geometry of the homogeneous space G/H [arxiv:gr-qc/0611154]. After explaining these geometric ideas, I explain a related formulation for Hamiltonian gravity, in which an observer field spontaneously breaks Lorentz symmetry to give ``Cartan geometrodynamics'': a system of evolving spatial Cartan geometries [arxiv:1111.7195]. Thanks to Cartan's ``method of equivalence'', this can be viewed as a link between geometrodynamics in the metric sense implemented by ADM and the connection dynamics of the Ashtekar formulation.