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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.09540 |
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| _version_ | 1866912792581242880 |
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| author | Zhang, Cong Cao, Zhoujian |
| author_facet | Zhang, Cong Cao, Zhoujian |
| contents | This work reveals a fundamental link between general covariance and Birkhoff's theorem. We extend Birkhoff's theorem from general relativity to a broad class of generally covariant gravity theories formulated in the Hamiltonian framework. Conversely, we show that each one-parameter family of static, spherically symmetric spacetimes determines a class of covariant theories, each of which has that family of spacetimes as its entire vacuum solution space. Our systematic and model-independent framework applies to a wide range of spacetimes, including observationally inferred, quantum-gravity-inspired, and regular black holes. It provides a universal tool for probing their dynamical origins and enables the reconstruction of the underlying covariant theories from observational data, including gravitational-wave and black-hole-shadow measurements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_09540 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Covariant dynamics from static spherically symmetric geometries Zhang, Cong Cao, Zhoujian General Relativity and Quantum Cosmology This work reveals a fundamental link between general covariance and Birkhoff's theorem. We extend Birkhoff's theorem from general relativity to a broad class of generally covariant gravity theories formulated in the Hamiltonian framework. Conversely, we show that each one-parameter family of static, spherically symmetric spacetimes determines a class of covariant theories, each of which has that family of spacetimes as its entire vacuum solution space. Our systematic and model-independent framework applies to a wide range of spacetimes, including observationally inferred, quantum-gravity-inspired, and regular black holes. It provides a universal tool for probing their dynamical origins and enables the reconstruction of the underlying covariant theories from observational data, including gravitational-wave and black-hole-shadow measurements. |
| title | Covariant dynamics from static spherically symmetric geometries |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2506.09540 |