Seminar

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.