Schwarzschild radial perturbations in Eddington-Finkelstein and Painlev\'e-Gullstrand coordinates

Understand

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 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.
• Firstly, we consider in Eddington-Finkelstein coordinates a massive scalar field that can serve as a dark matter candidate.