Resonance expansions of massless Dirac fields propagating in the exterior of a de Sitter–Reissner–Nordström black hole

We give an expansion of the solution of the evolution equation for the massless Dirac fields in the outer region of deSitter–Reissner–Nordström black hole in terms of resonances. By means of this method we describe the decay of local energy for compactly supported data. The proof uses the cut-off resolvent estimates for the semi-classical Schrödinger operators from [4]. The method extends to the Dirac operators on spherically symmetric asymptotically hyperbolic manifolds