Are gauge shocks really shocks?

TL;DR

This paper proves that certain gauge pathologies in 1+1 relativity are genuine shocks, where characteristic lines cross, leading to non-smooth spacetime foliations, confirming the term "gauge shock" is appropriate.

Contribution

It demonstrates that gauge pathologies in the Bona-Masso slicing conditions are actual shocks, providing a rigorous proof in a simplified relativity setting.

Findings

Gauge shocks are true shocks with crossing characteristic lines.

Gauge shocks cause non-smooth spacetime foliation.

The term 'gauge shock' is validated as appropriate.

Abstract

The existence of gauge pathologies associated with the Bona-Masso family of generalized harmonic slicing conditions is proven for the case of simple 1+1 relativity. It is shown that these gauge pathologies are true shocks in the sense that the characteristic lines associated with the propagation of the gauge cross, which implies that the name ``gauge shock'' usually given to such pathologies is indeed correct. These gauge shocks are associated with places where the spatial hypersurfaces that determine the foliation of spacetime become non-smooth.