Field propagation in de Sitter black holes

We present an exhaustive analysis of scalar, electromagnetic, and gravitational perturbations in the background of Schwarzchild–de Sitter and Reissner–Nordström–de Sitter spacetimes. The field propagation is considered by means of a semianalytical (WKB) approach and two numerical schemes: the characteristic and general initial value integrations. The results are compared near the extreme cosmological constant regime, where analytical results are presented. A unifying picture is established for the dynamics of different spin fields.