Gravitational collapse of K-essence Matter in Painlev\'{e}-Gullstrand coordinates

Understand

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.