Pathologies of hyperbolic gauges in general relativity and other field theories

TL;DR

This paper analyzes how non-linear hyperbolic gauge choices can cause blow-ups in solutions of general relativity and electrodynamics, providing mathematical characterization, numerical detection methods, and discussing implications for numerical relativity.

Contribution

It offers a mathematical framework for understanding hyperbolic gauge pathologies and demonstrates numerical techniques to identify and analyze these blow-ups.

Findings

Non-linear gauge terms can cause solution blow-ups along characteristics.

Convergence analysis can detect gauge pathologies numerically.

Numerical examples illustrate the impact on numerical relativity.

Abstract

We present a mathematical characterization of hyperbolic gauge pathologies in general relativity and electrodynamics. We show how non-linear gauge terms can produce a blow-up along characteristics and how this can be identified numerically by performing convergence analysis. Finally, we show some numerical examples and discuss the profound implications this may have for the field of numerical relativity.