Pathologies of hyperbolic gauges in general relativity and other field theories

We present a mathematical characterization of hyperbolic gauge pathologies in electrodynamics and general relativity. We show analytically how non-linear gauge terms can produce a blow-up of some fields along characteristics. We expect similar phenomena to appear in any other gauge field theory. We also present numerical simulations where such blow-ups develop and show how they can be properly identified by performing a convergence analysis. We stress the importance of these results for the particular case of numerical relativity, where we offer some cures based on the use of non-hyperbolic gauges.