Resonance expansions of massless Dirac fields propagating in the exterior of a de Sitter-Reissner-Nordstr\"om black hole

TL;DR

This paper develops a resonance expansion method for massless Dirac fields around de Sitter-Reissner-Nordström black holes, providing insights into their energy decay and extending techniques to similar geometric settings.

Contribution

It introduces a resonance expansion approach for Dirac fields in black hole spacetimes, linking spectral analysis with decay properties and extending to hyperbolic manifolds.

Findings

Resonance expansion describes Dirac field evolution.

Decay of local energy for compact data is characterized.

Method applies to spherically symmetric asymptotically hyperbolic manifolds.

Abstract

We give an expansion of the solution of the evolution equation for the massless Dirac fields in the outer region of de Sitter-Reissner-Nordstr\"om 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 Schr\"odinger operators from Bony and H\"afner, 2008. The method extends to the Dirac operators on spherically symmetric asymptotically hyperbolic manifolds.