Evolution of Brill waves with an adaptive pseudospectral method

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.

11 pages, 7 figures

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• Simulating binary black hole mergers using discontinuous Galerkin methods
• Critical phenomena in gravitational collapse with competing scalar field and gravitational waves, in 4+1 dimensions
• Twist and higher modes of a complex scalar field at the threshold of collapse
• Brill Waves with Slow Fall-Off Towards Spatial Infinity
• Pseudospectral implementation of the Einstein-Maxwell system