Formation of Trapped Surfaces in Geodesic Foliation
Abstract
We revisit the classical results of the formation of trapped surfaces for the Einstein vacuum equation relying on the geodesic foliation, rather than the double null foliation used in all previous results, starting with the seminal work of Christodoulou Chr1 and continued in KRodn, An, AnLuk, KLR, An1. The main advantage of the method is that it only requires information on the incoming curvature along the incoming initial null hypersurface. The result is based on a version of the non-integrable PT frame introduced in KS:Kerr and GKS, associated to the geodesic foliation.
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