Evolution of Brill waves with an adaptive pseudospectral method

TL;DR

This paper uses an adaptive pseudospectral method to evolve Brill gravitational waves near collapse threshold, revealing new insights into curvature behavior and apparent horizon formation in axisymmetric spacetimes.

Contribution

It introduces a new adaptive mesh functionality in the pseudospectral code bamps and applies it to study off-centered Brill wave initial data, expanding understanding of gravitational wave collapse.

Findings

Curvature peaks form away from the origin near collapse threshold.

Evidence suggests no strict discrete self-similarity or universal power-law scaling.

Universal strong curvature features are observed across all families.

Abstract

As a first application of the new adaptive mesh functionality of the the pseudospectral numerical relativity code bamps, we evolve twist-free, axisymmetric gravitational waves close to the threshold of collapse. We consider six different one-parameter families of Brill wave initial data; two centered and four off-centered families. Of these the latter have not been treated before. Within each family we tune the parameter towards the threshold of black hole formation. The results for centered data agree with earlier work. Our key results are first, that close to the threshold of collapse the global peak in the curvature appears on the symmetry axis but away from the origin, indicating that in the limit they will collapse around disjoint centers. This is confirmed in three of the six families by explicitly finding apparent horizons around these large curvature peaks. Second, we find evidence neither for strict discrete-self-similarity nor for universal power-law scaling of curvature quantities. Finally, as in Ledvinka & Khirnov's recent study, we find approximately universal strong curvature features. These features appear multiple times within individual spacetimes close to the threshold and are furthermore present within all six families.