  The family of generalized-harmonic gauge conditions, which is currently used
in Numerical Relativity for its singularity-avoidant behavior, is analyzed by
looking for pathologies of the corresponding spacetime foliation. The
appearance of genuine shocks, arising from the crossing of characteristic
lines, is completely discarded. Runaway solutions, meaning that the lapse
function can grow without bound at an accelerated rate, are instead predicted.
Black Hole simulations are presented, showing spurious oscillations due to the
well known slice stretching phenomenon. These oscillations are made to
disappear by switching the numerical algorithm to a high-resolution
shock-capturing one, of the kind currently used in Computational Fluid
Dynamics. Even with these shock-capturing algorithms, runaway solutions are
seen to appear and the resulting lapse blow-up is causing the simulations to
crash. As a side result, a new method is proposed for obtaining regular initial
data for Black Hole spacetimes, even inside the horizons.
