Spherically Symmetric Black Hole Formation in Painlevé-Gullstrand Coordinates

Abstract

We perform a numerical study of black hole formation from the spherically symmetric collapse of a massless scalar field. The calculations are done in Painlevé-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. The subcritical curvature scaling exhibits the expected oscillatory behaviour but the form of the periodic oscillations in the supercritical mass scaling relation, while universal with respect to initial PG data, is non-standard: it is non-sinusoidal with large amplitude cusps.

12 pages, 7 figures

References in corpus (4)

• Loop Quantum Dynamics of the Schwarzschild Interior
• Black holes in loop quantum gravity: the complete space-time
• Transgressing the horizons: Time operator in two-dimensional dilaton gravity
• Critical behaviour in quantum gravitational collapse

Cited by in corpus (10)

• Scalarized Black Hole dynamics in Einstein dilaton Gauss-Bonnet Gravity
• Dynamics of a Z2 symmetric EdGB gravity in spherical symmetry
• Dynamical Singularity Resolution in Spherically Symmetric Black Hole Formation
• MOTS in Schwarzschild: multiple self-intersections and extreme mass ratio mergers
• Dynamical scalarization in Einstein-Maxwell-dilaton theory
• 3D gravity with dust: classical and quantum theory
• Closest Safe Approach to an Accreting Black Hole
• Black Hole Formation in Lovelock Gravity
• Ideal hydrodynamics inside as well as outside non-rotating black hole: Hamiltonian description in the Painlev{é}-Gullstrand coordinates
• Directly observing entropy accumulate on the horizon and holography