Numerical study of black-hole formation in Painlevé-Gullstrand coordinates

We study numerically black-hole formation from a collapsing massless scalar field. The use of Painlevé-Gullstrand coordinates allows the evolution to proceed until singularity formation. We generate spacetime maps of the collapse, illustrating the evolution of apparent horizons for various initial data. A study of the Choptuik scaling reveals the expected universal values for the critical exponent and echoing period. The periodic oscillations in the supercritical horizon scaling relation, while universal with respect to initial Painlevé-Gullstrand data, show unexpected structure with large amplitude cusps.