  We conduct numerical simulations in Painlev\'{e}-Gullstrand coordinates of a
variety of K-essence-type scalar fields under spherically symmetric
gravitational collapse. We write down generic conditions on the K-essence
lagrangian that can be used to determine whether superluminality and Cauchy
breakdown are possible. Consistent with these conditions, for specific choices
of K-essence-type fields we verify the presence of superluminality during
collapse, while for other type we do not. We also demonstrate that certain
choices of K-essence scalar fields present issues under gravitational collapse
in Painlev\'{e}-Gullstrand coordinates, such as a breakdown of the Cauchy
problem.
