Puncture Evolution of Schwarzschild Black Holes

Abstract

The moving puncture method is analyzed for a single, non-spinning black hole. It is shown that the puncture region is not resolved by current numerical codes. As a result, the geometry near the puncture appears to evolve to an infinitely long cylinder of finite areal radius. The puncture itself actually remains at spacelike infinity throughout the evolution. In the limit of infinite resolution the data never become stationary. However, at any reasonable finite resolution the grid points closest to the puncture are rapidly drawn into the black hole interior by the Gamma-driver shift condition. The data can then evolve to a stationary state. These results suggest that the moving puncture technique should be viewed as a type of "natural excision".

This is the final version to be published in PRD. One important change: the phrase "excision by under resolution" is replaced by the more appropriate phrase "natural excision"

References in corpus (3)

• Binary black hole mergers: large kicks for generic spin orientations
• Analytical Representation of a Black Hole Puncture Solution
• Are moving punctures equivalent to moving black holes?

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• BSSN in Spherical Symmetry
• Comments on Bona-Masso type slicing conditions in long-term black hole evolutions