Long-term 3+1 simulations of primordial black hole formation during radiation domination
Abstract
We develop an efficient three-dimensional numerical-relativity framework for primordial black-hole (PBH) formation from superhorizon curvature perturbations in a radiation-dominated Universe. We implement flux-conservative relativistic hydrodynamics in the adaptive-mesh-refinement code \textsc{GRChombo} and introduce a cosmologically scaled Gamma-driver that allows the cosmic-time step to grow in proportion to the scale factor. For a representative long-term simulation, the scaled driver preserves the apparent-horizon mass evolution and constraint behavior while reducing the number of coarse-level advances by a factor of approximately $94$ relative to the standard driver. We also construct a conformal-time version of the moving-puncture gauge as an independent check. Applying the framework to a spherical Gaussian curvature profile, we find a collapse threshold 0.79578 < μc < 0.79580 and a critical exponent γ≃ 0.3559, consistent with previous spherically symmetric results. We further fit the late-time PBH mass growth to the Zel'dovich--Novikov accretion law, demonstrating that the code can follow both near-critical collapse and long-term post-formation evolution in three dimensions. The framework provides a foundation for future studies of PBH formation beyond spherical symmetry.
Related
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BibTeX
@misc{ning2026longterm,
title = {{Long-term 3+1 simulations of primordial black hole formation during radiation domination}},
author = {Zhuan Ning and Rong-Gen Cai and Shao-Jiang Wang and Chul-Moon Yoo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.13206},
eprint = {2608.13206},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.13206},
}
RIS
TY - UNPB
TI - Long-term 3+1 simulations of primordial black hole formation during radiation domination
AU - Zhuan Ning
AU - Rong-Gen Cai
AU - Shao-Jiang Wang
AU - Chul-Moon Yoo
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2608.13206
UR - https://arxiv.org/abs/2608.13206
AB - We develop an efficient three-dimensional numerical-relativity framework for primordial black-hole (PBH) formation from superhorizon curvature perturbations in a radiation-dominated Universe. We implement flux-conservative relativistic hydrodynamics in the adaptive-mesh-refinement code \textsc{GRChombo} and introduce a cosmologically scaled Gamma-driver that allows the cosmic-time step to grow in proportion to the scale factor. For a representative long-term simulation, the scaled driver preserves the apparent-horizon mass evolution and constraint behavior while reducing the number of coarse-level advances by a factor of approximately $94$ relative to the standard driver. We also construct a conformal-time version of the moving-puncture gauge as an independent check. Applying the framework to a spherical Gaussian curvature profile, we find a collapse threshold 0.79578 < μ_c < 0.79580 and a critical exponent γ≃ 0.3559, consistent with previous spherically symmetric results. We further fit the late-time PBH mass growth to the Zel'dovich--Novikov accretion law, demonstrating that the code can follow both near-critical collapse and long-term post-formation evolution in three dimensions. The framework provides a foundation for future studies of PBH formation beyond spherical symmetry.
ER -