The close limit from a null point of view: the advanced solution

TL;DR

This paper introduces a characteristic algorithm for computing black hole perturbations using the Teukolsky equation, successfully modeling the advanced solution in black hole collisions with high precision over many orders of magnitude.

Contribution

It presents a novel characteristic evolution code for the Teukolsky equation to compute the advanced solution in black hole perturbations, enabling detailed waveform analysis.

Findings

Successfully tracks initial burst and quasinormal decay over 10 orders of magnitude.

Accurately models the final power law decay over an additional 6 orders of magnitude.

First to determine the advanced solution with ingoing radiation absorption and no outgoing radiation.

Abstract

We present a characteristic algorithm for computing the perturbation of a Schwarzschild spacetime by means of solving the Teukolsky equation. We implement the algorithm as a characteristic evolution code and apply it to compute the advanced solution to a black hole collision in the close approximation. The code successfully tracks the initial burst and quasinormal decay of a black hole perturbation through 10 orders of magnitude and tracks the final power law decay through an additional 6 orders of magnitude. Determination of the advanced solution, in which ingoing radiation is absorbed by the black hole but no outgoing radiation is emitted, is the first stage of a two stage approach to determining the retarded solution, which provides the close approximation waveform with the physically appropriate boundary condition of no ingoing radiation.