Speaker
Poul Tod
(Oxford)
Description
One knows, for example by proving well-posedness for an initial value problem with
data at the singularity, that there exist many cosmological solutions of the
Einstein equations with an initial curvature singularity but for which the
conformal metric can be extended through the singularity. Here we consider a
converse, a local extension problem for the conformal structure: given an
incomplete causal curve terminating at a curvature singularity, when can one
extend the conformal structure to a set containing a neighbourhood of a final
segment of the curve? We obtain necessary and sufficient conditions based on
boundedness of tractor curvature components. (Based on work with Christian Luebbe:
arXiv:0710.5552, arXiv:0710.5723.)
