Speaker
Hubert Bray
(Duke)
Description
The proofs of the Riemannian Penrose Conjecture by Huisken-Ilmanen in
1997 (for one black hole) and by the speaker in 1999 (for any number of
black holes) describe the geometric relationships between the total mass
of a slice of a spacetime and the size and number of black holes in the
slice, in the special case that the slice has zero second fundamental
form in the spacetime. However, Penrose's original 1973 conjecture
concerns any asymptotically flat, space-like slice of a spacetime and,
consequently, is still open in its most general form. In this talk, the
speaker will describe a joint effort with Marcus Khuri to reduce the
general case of the Penrose Conjecture to the known case using a
generalization of Jang's equation (used to prove the general case of the
positive mass theorem) and a new geometric identity, which we are
calling the generalized Schoen-Yau identity, which is designed to
recognize arbitrary space-like slices of static spacetimes (like the
Schwarzschild spacetime, which is the case of equality of the Penrose
Conjecture), and hence is ideally suited for our purposes. We will then
discuss three different systems of p.d.e.s whose solutions, when they
exist, imply the Penrose Conjecture.
