Caltech/UCLA Joint Analysis Seminar

I will review stability results for the evolution of linear waves on subextremal black holes and then present stability and instability results for the extremal (i.e. critical) case. The source of the instability results is a hierarchy of conservation laws along the extremal event hotizon. I will provide necessary and sufficient conditions for the existence of such conservation laws on general null hypersurfaces in Lorentzian manifolds and also show that these laws are in fact the only obstruction to gluing of characteristic initial data for the wave equation. I will start with a short introduction to general relativity and hence no prior knowledge of that field is required.