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PreprintCC BY 4.0arXiv

Static Vacuum Geometry Encodes Gravitational Collapse and Cosmology

  • Yi Ling
  • Jinsong Yang
  • Zhangping Yu
  • Cong Zhang
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Abstract

We show that, within covariant Hamiltonian gravity in spherical symmetry, a prescribed one-parameter family of static vacuum geometries uniquely determines the local dynamics of gravitational collapse coupled to irrotational dust, despite the nonuniqueness of the underlying gravitational Hamiltonian. We further derive necessary and sufficient conditions under which the resulting dynamics admits a homogeneous and isotropic cosmological sector. These conditions establish a two-way correspondence between static vacuum geometries and modified Friedmann dynamics and impose a universal restriction on the spatial-curvature dependence of the latter. Our results provide a criterion for determining whether independently proposed black-hole and cosmological models can arise from a common covariant gravitational theory.

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Cite

BibTeXRIS
BibTeX
@misc{ling2026static,
  title = {{Static Vacuum Geometry Encodes Gravitational Collapse and Cosmology}},
  author = {Yi Ling and Jinsong Yang and Zhangping Yu and Cong Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.02358},
  eprint = {2611.02358},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.02358},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Static Vacuum Geometry Encodes Gravitational Collapse and Cosmology
AU  - Yi Ling
AU  - Jinsong Yang
AU  - Zhangping Yu
AU  - Cong Zhang
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.02358
UR  - https://arxiv.org/abs/2611.02358
AB  - We show that, within covariant Hamiltonian gravity in spherical symmetry, a prescribed one-parameter family of static vacuum geometries uniquely determines the local dynamics of gravitational collapse coupled to irrotational dust, despite the nonuniqueness of the underlying gravitational Hamiltonian. We further derive necessary and sufficient conditions under which the resulting dynamics admits a homogeneous and isotropic cosmological sector. These conditions establish a two-way correspondence between static vacuum geometries and modified Friedmann dynamics and impose a universal restriction on the spatial-curvature dependence of the latter. Our results provide a criterion for determining whether independently proposed black-hole and cosmological models can arise from a common covariant gravitational theory.
ER  -