Wave and Dirac equations on manifolds

Abstract

We review some recent results on geometric equations on Lorentzian manifolds such as the wave and Dirac equations. This includes well-posedness and stability for various initial value problems, as well as results on the structure of these equations on black-hole spacetimes (in particular, on the Kerr solution), the index theorem for hyperbolic Dirac operators and properties of the class of Green-hyperbolic operators.

21 pages, 1 figure

References in corpus (2)

• An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary
• New identities for linearized gravity on the Kerr spacetime