Numerical stability of the AA evolution system compared to the ADM and BSSN systems

TL;DR

This paper compares the numerical stability of the Alekseenko-Arnold evolution system with ADM and BSSN systems through standardized tests and black hole simulations, highlighting strengths and limitations of these methods.

Contribution

It provides the first systematic stability comparison of the Alekseenko-Arnold system against established formulations like ADM and BSSN.

Findings

Alekseenko-Arnold system shows competitive stability in testbeds.

Differences in gauge choices affect stability outcomes.

Standardized tests may not fully predict stability in complex scenarios.

Abstract

We explore the numerical stability properties of an evolution system suggested by Alekseenko and Arnold. We examine its behavior on a set of standardized testbeds, and we evolve a single black hole with different gauges. Based on a comparison with two other evolution systems with well-known properties, we discuss some of the strengths and limitations of such simple tests in predicting numerical stability in general.