  I consider the appearance of shocks in hyperbolic formalisms of General
Relativity. I study the particular case of the Bona-Masso formalism with zero
shift vector and show how shocks associated with two families of characteristic
fields can develop. These shocks do not represent discontinuities in the
geometry of spacetime, but rather regions where the coordinate system becomes
pathological. For this reason I call them coordinate shocks. I show how one
family of shocks can be eliminated by restricting the Bona-Masso slicing
condition to a special case. The other family of shocks, however, can not be
eliminated even in the case of harmonic slicing. I also show the results of
numerical simulations in the special cases of a flat two-dimensional spacetime,
a flat four-dimensional spacetime with a spherically symmetric slicing, and a
spherically symmetric black hole spacetime. In all three cases coordinate
shocks readily develop, confirming the predictions of the mathematical
analysis. Although here I concentrate in the Bona-Masso formalism, the
phenomena of coordinate shocks should arise in any other hyperbolic formalism.
In particular, since the appearance of the shocks is determined by the choice
of gauge, the results presented here imply that in any formalism the use of a
harmonic slicing can generate shocks.
