Black Hole--Scalar Field Interactions in Spherical Symmetry

TL;DR

This paper studies black hole interactions with a massless scalar field in dynamic spherical spacetimes, using a stable numerical scheme to observe phenomena like quasi-normal ringing and tails.

Contribution

It introduces a stable, convergent numerical method for simulating black hole-scalar field interactions in dynamic spherical symmetry.

Findings

Observation of quasi-normal ringing

Detection of power-law tails

Identification of nonlinear features

Abstract

We examine the interactions of a black hole with a massless scalar field using a coordinate system which extends ingoing Eddington-Finkelstein coordinates to dynamic spherically symmetric-spacetimes. We avoid problems with the singularity by excising the region of the black hole interior to the apparent horizon. We use a second-order finite difference scheme to solve the equations. The resulting program is stable and convergent and will run forever without problems. We are able to observe quasi-normal ringing and power-law tails as well an interesting nonlinear feature.