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General Relativity and Quantum Cosmology, gr-qc
Abstract:
We develop a numerical method suitable for gravitational collapse based on
Cauchy evolution with an ingoing characteristic boundary. Unlike similar
methods proposed recently (Ripley; Bieri, Garfinkle & Yau 2019/20), 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 1993) are
reproduced using this considerably simpler numerical method.
