Spherically Symmetric Black Hole Formation in Painlev\'e-Gullstrand Coordinates

Understand

We perform a numerical study of black hole formation from the spherically symmetric collapse of a massless scalar field.

• The calculations are done in Painlev\'e-Gullstrand (PG) coordinates that extend across apparent horizons and allow the numerical evolution to proceed until the onset of singularity formation.
• We generate spacetime maps of the collapse and illustrate the evolution of apparent horizons and trapping surfaces for various initial data.
• We also study the critical behaviour and find the expected Choptuik scaling with universal values for the critical exponent and echoing period consistent with the accepted values of $\gamma=0.374$ and $\Delta = 3.44$, respectively.