Abstract

Reliable numerical simulations require a thorough control of all non-physical dynamics that can appear, such as constraint violations and coordinate singularities. These become more challenging in the strong-field regime and particularly near the threshold of collapse, where, in the absence of a horizon, arbitrarily large curvatures cannot be excised. At this threshold, a regular and universal structure emerges in spherical symmetry, referred to as critical phenomena. Beyond sphericity, the picture of critical collapse is unclear. Clarification demands simulations that are closer to the threshold. To that end, we propose two formulation improvements for critical collapse simulations. To control constraint violations, we modify the constraint damping parameters of the generalised harmonic gauge formulation, adapting them to collapsing spacetimes. This allows us to simulate at the closest to the threshold with this formulation to date. Secondly, we propose a necessary condition for a gauge choice to respect discrete self-similarity. After evaluating common gauge choices against this condition, we suggest a compatible gauge source function.