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

TL;DR

This paper uses numerical simulations in Painleve-Gullstrand coordinates to study gravitational collapse of K-essence scalar fields, identifying conditions for superluminality and Cauchy breakdown during collapse.

Contribution

It establishes generic conditions on K-essence Lagrangians to predict superluminality and Cauchy breakdown, and verifies these phenomena through simulations.

Findings

Superluminality occurs for certain K-essence fields during collapse.

Some K-essence fields cause Cauchy problem breakdown in collapse.

Conditions on Lagrangians predict superluminality and breakdown phenomena.

Abstract

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.