In a previous paper, we have considered the Regge–Wheeler equation for fields of spin s = 0, 1 or 2 on the Schwarzschild spacetime in coordinates that are regular at the horizon. In particular, we have constructed in Eddington–Finkelstein (EF) coordinates exact solutions in terms of series that are regular at the horizon and converge on the entire open domain from the central singularity to infinity. Here, we extend this earlier work in two different directions. First, we consider in EF coordinates a massive scalar field that can serve as a dark matter candidate. Second, we extend the treatment of the massless case to Painlevé–Gullstrand (PG) coordinates, which are associated with radially infalling observers.
Study of a Scalar Field on the Maximally Extended Schwarzschild Spacetime
