Critical collapse of vacuum spacetimes: Nakamura wave initial data
Abstract
We report on numerical simulations of critical phenomena in the collapse of axisymmetric vacuum gravitational waves, adopting families of initial data that, to the best of our knowledge, have not been used in this context before. Like Teukolsky waves, the data are based on linear wave solutions to the Einstein equations. We follow Nakamura's construction and encode the wave content in the extrinsic curvature rather than the spatial curvature, which leads to several simplifications when the data are "dressed up" so that they satisfy the nonlinear constraint equations. We are able to fine-tune these data to the onset of black hole formation slightly better than in our previous simulations, allowing us to observe and examine one more echo in the approximately self-similar threshold solution. Our findings are consistent with earlier studies: while we find threshold solutions that are approximately discretely self-similar, the self-similarity is not exact, and we find no evidence for a unique critical solution. We discuss common features between the different threshold solutions, including the appearance of alternating maxima in the direction of the poles and the equator.
Related
- Angular Momenta in 4+1 Vacuum Critical Collapse
- Nonexistence of Multiple Black Holes in Stationary Analytic Vacuum spacetimes
- Initial Data Gluing for Asymptotically Hyperbolic Spacetimes
- Swirling spacetimes in higher dimensions: Vacuum backgrounds and black holes
- Static Vacuum Geometry Encodes Gravitational Collapse and Cosmology
BibTeX
@misc{baumgarte2026critical,
title = {{Critical collapse of vacuum spacetimes: Nakamura wave initial data}},
author = {Thomas W. Baumgarte and Carsten Gundlach and David Hilditch},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2606.27431},
eprint = {2606.27431},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.27431},
}
RIS
TY - UNPB
TI - Critical collapse of vacuum spacetimes: Nakamura wave initial data
AU - Thomas W. Baumgarte
AU - Carsten Gundlach
AU - David Hilditch
PY - 2026
DA - 2026/08/11
PB - arXiv
DO - 10.48550/arxiv.2606.27431
UR - https://arxiv.org/abs/2606.27431
AB - We report on numerical simulations of critical phenomena in the collapse of axisymmetric vacuum gravitational waves, adopting families of initial data that, to the best of our knowledge, have not been used in this context before. Like Teukolsky waves, the data are based on linear wave solutions to the Einstein equations. We follow Nakamura's construction and encode the wave content in the extrinsic curvature rather than the spatial curvature, which leads to several simplifications when the data are "dressed up" so that they satisfy the nonlinear constraint equations. We are able to fine-tune these data to the onset of black hole formation slightly better than in our previous simulations, allowing us to observe and examine one more echo in the approximately self-similar threshold solution. Our findings are consistent with earlier studies: while we find threshold solutions that are approximately discretely self-similar, the self-similarity is not exact, and we find no evidence for a unique critical solution. We discuss common features between the different threshold solutions, including the appearance of alternating maxima in the direction of the poles and the equator.
ER -