The characteristic gluing problem for the wave equation and applications
The characteristic gluing problem for the wave equation and applications

Stefanos Aretakis , Princeton University
Fine Hall 314
We will first describe the characteristic gluing problem for the wave equation on a general fourdimensional 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 2spheres of a null hypersurface. We will finally present some applications to black hole spacetimes.