Toronto, 6 - 9 décembre 2019
In this talk I will outline a constructive approach to proving the existence of apparent horizons. In particular, I will consider a distinguished family of spacelike hypersurfaces in the maximally extended Schwarzschild spacetime, and prove that Jang's equation admits no global solutions once the hypersurfaces become sufficiently close to the r=0 singularity. This suggests a general strategy for relating spacetime singularities to apparent horizons. This is joint work with Amir Aazami.
See preprint at http://www.math.toronto.edu/mccann/papers/GRO.pdf