Simulations with Nakamura wave initial data confirm approximately discretely self-similar threshold solutions in vacuum gravitational wave collapse, but without exact self-similarity or a unique critical solution, consistent with prior studies.
Constrained evolution in axisymmetry and the gravitational collapse of prolate Brill waves
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abstract
This paper is concerned with the Einstein equations in axisymmetric vacuum spacetimes. We consider numerical evolution schemes that solve the constraint equations as well as elliptic gauge conditions at each time step. We examine two such schemes that have been proposed in the literature and show that some of their elliptic equations are indefinite, thus potentially admitting nonunique solutions and causing numerical solvers based on classical relaxation methods to fail. A new scheme is then presented that does not suffer from these problems. We use our numerical implementation to study the gravitational collapse of Brill waves. A highly prolate wave is shown to form a black hole rather than a naked singularity.
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gr-qc 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Critical collapse of vacuum spacetimes: Nakamura wave initial data
Simulations with Nakamura wave initial data confirm approximately discretely self-similar threshold solutions in vacuum gravitational wave collapse, but without exact self-similarity or a unique critical solution, consistent with prior studies.