Testing the well-posedness of characteristic evolution of scalar waves

TL;DR

This paper investigates how lower order terms influence the well-posedness of characteristic evolution for scalar waves, providing theoretical insights and implementing a stable finite difference algorithm validated through tests.

Contribution

It introduces a finite difference implementation of recent theoretical results on well-posedness influenced by lower order terms in scalar wave evolution.

Findings

The code is stable and accurately models scalar wave evolution.

Lower order terms can be tuned to ensure well-posedness.

Test results demonstrate the impact of these terms on stability.

Abstract

Recent results have revealed a critical way in which lower order terms affect the well-posedness of the characteristic initial value problem for the scalar wave equation. The proper choice of such terms can make the Cauchy problem for scalar waves well posed even on a background spacetime with closed lightlike curves. These results provide new guidance for developing stable characteristic evolution algorithms. In this regard, we present here the finite difference version of these recent results and implement them in a stable evolution code. We describe test results which validate the code and exhibit some of the interesting features due to the lower order terms.