The characteristic gluing problem for the wave equation and applications

Monday, September 16, 2013 -
3:15pm to 4:15pm
We will first describe the characteristic gluing problem for the wave equation on a general four-dimensional Lorentzian manifold. We will show that the only obstruction to such gluing constructions is in fact the existence of certain ``conservation laws''  on null hypersurfaces and we will then obtain necessary and sufficient conditions for the existence of such conservation laws. Our method relies on a novel elliptic structure associated to a foliation with 2-spheres of a null hypersurface. We will finally present some applications to black hole spacetimes.
Speaker: 
Stefanos Aretakis
Princeton University
Event Location: 
Fine Hall 314