Analytical and numerical treatment of perturbed black holes in horizon-penetrating coordinates

Understand

The deviations of non-linear perturbations of black holes from the linear case are important in the context of ringdown signals with large signal-to-noise ratio.

• To facilitate a comparison between the two we derive several results of linear perturbation theory in coordinates which may be adopted in numerical work.
• Specifically, our results are derived in Kerr-Schild coordinates adjusted by a general height function.
• In the first part of the paper we address the questions: for an initial configuration of a massless scalar field, what is the amplitude of the excited quasinormal mode (QNM) for any observer outside outside the event horizon, and furthermore what is the resulting tail contribution? This is done by constructing the full Green's function for the problem with exact solutions of the confluent Heun equation satisfying appropriate boundary conditions.