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 de Sitter-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.