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Seminar

MGR Programmatic Seminar: Geometric Boundary Data for the Gravitational Field November 07, 2013 (01:30 PM PST - 02:30 PM PST)
Parent Program: Mathematical General Relativity
Location: MSRI: Simons Auditorium
Speaker(s) Jeffrey Winicour (University of Pittsburgh)
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An outstanding issue in the treatment of boundaries in general relativity has been the lack of a local geometric interpretation of the necessary boundary data. For the Cauchy problem, the initial data is supplied by the 3-metric and extrinsic curvature of the initial Cauchy hypersurface, subject to constraints. This Cauchy data determine a solution to Einstein's equations which is unique up to diffeomorphism.  I will describe how three pieces of unconstrained boundary data, which are associated locally with the geometry of the boundary, likewise determine a solution of the initial-boundary value problem which is unique, up to diffeomorphism. Two pieces of this data constitute a conformal class of rank-2 metrics, which represent the two gravitational degrees of freedom. The third piece, constructed from the extrinsic curvature of the boundary, determines the dynamical evolution of the boundary.

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