Field propagation in the Schwarzschild-de Sitter black hole

We present an exhaustive analysis of scalar, electromagnetic and gravitational perturbations in the background of a Schwarzchild-de Sitter spacetime. The field propagation is considered by means of a semi-analytical (WKB) approach and two numerical schemes: the characteristic and general initial value integrations. The results are compared near the extreme regime, and a unifying picture is established for the dynamics of different spin fields. Although some of the results just confirm usual expectations, a few surprises turn out to appear, as the dependence on the non-characteristic initial conditions of the non-vanishing asymptotic value for l=0 mode scalar fields.