Gravitational waveforms with controlled accuracy

TL;DR

This paper introduces a new first-order characteristic formulation for computing gravitational waveforms from distorted black holes, significantly improving accuracy in highly nonlinear regimes.

Contribution

It develops a partially first-order form of the characteristic formulation that enhances accuracy in gravitational waveform calculations for complex black hole spacetimes.

Findings

Improved accuracy over standard methods in post-merger black hole simulations.

Effective control of numerical errors in highly nonlinear regimes.

Enhanced reliability of gravitational waveform predictions.

Abstract

A partially first-order form of the characteristic formulation is introduced to control the accuracy in the computation of gravitational waveforms produced by highly distorted single black hole spacetimes. Our approach is to reduce the system of equations to first-order differential form on the angular derivatives, while retaining the proven radial and time integration schemes of the standard characteristic formulation. This results in significantly improved accuracy over the standard mixed-order approach in the extremely nonlinear post-merger regime of binary black hole collisions.