# The characteristic gluing problem for the wave equation and applications

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Stefanos Aretakis , Princeton University
Fine Hall 314

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.