On the non-linearity of the subsidiary systems

TL;DR

This paper investigates non-linearities in subsidiary systems of hyperbolic Einstein equations reductions, highlighting potential risks of catastrophic growth in gauge and constraint violations during numerical simulations.

Contribution

It identifies a class of non-linearities in subsidiary systems that could cause instability in numerical solutions of Einstein equations.

Findings

Non-linearities can lead to exponential growth of violations.

Certain subsidiary system structures are more prone to instabilities.

Awareness of these non-linearities can improve numerical stability strategies.

Abstract

In hyperbolic reductions of the Einstein equations the evolution of gauge conditions or constraint quantities is controlled by subsidiary systems. We point out a class of non-linearities in these systems which may have the potential of generating catastrophic growth of gauge resp. constraint violations in numerical calculations.