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arXiv · 2506.09540

Covariant dynamics from static spherically symmetric geometries

Cong Zhang·Zhoujian Cao
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Abstract

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.

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Cong Zhang, Zhoujian Cao. 2025-06-11. Covariant dynamics from static spherically symmetric geometries. https://doi.org/10.1103/6sws-hfj7

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