Type II critical collapse on a single fixed grid: a gauge-driven ingoing boundary method

Abstract

AbstractWe develop a numerical method suitable for gravitational collapse based on Cauchy evolution with an ingoing characteristic boundary. Unlike similar methods proposed recently (Ripley; Bieri et al. in Class Quantum Grav 37:045015, 2020), the numerical grid remains fixed during the evolution and no points need to be removed or added. Increasing coordinate refinement of the central region as the field collapses is achieved solely through the choice of spatial gauge and particularly its boundary condition. We apply this method to study critical collapse of a massless scalar field in spherical symmetry using maximal slicing and isotropic coordinates. Known results on mass scaling, discrete self-similarity and universality of the critical solution (Choptuik in Phys Rev Lett 70:9, 1993) are reproduced using this considerably simpler numerical method.