Scaling the extrinsic curvature in the gravitational initial data: Generating trapped surfaces
National University of Ireland, Cork
In the standard conformal method of constructing initial data for the Einstein equations, the `free' data is chosen to be a base Riemannian 3-metric and a divergenceless, tracefree tensor (TT) relative to this metric. One then gets a non-linear elliptic equation (the Lichnerowicz equation) for a conformal factor. If I take a TT tensor and multiply it by a constant, it is still TT. One can show that the conformal factor monotonically increases as this constant is increased. In particular, the ADM mass of the solution becomes unboundedly large. This forces the appearance of trapped surfaces in the intial data. This will be a `low-tech' talk, showing how one can prove interesting results using nothing but the maximum principle.
Thursday, June 2, 2011
11:00AM AP&M 5829
Center for Computational Mathematics9500 Gilman Dr. #0112La Jolla, CA 92093-0112Tel: (858)534-9056