Covariant dynamics from static spherically symmetric geometries

TL;DR

This paper establishes a universal, model-independent framework linking general covariance to Birkhoff's theorem, allowing the reconstruction of covariant gravity theories from static, spherically symmetric spacetime data.

Contribution

It extends Birkhoff's theorem to a broad class of covariant gravity theories in the Hamiltonian framework and shows how static solutions determine entire classes of covariant theories.

Findings

Framework applies to observationally inferred and quantum-inspired black holes.

Enables reconstruction of underlying theories from gravitational-wave and black-hole-shadow data.

Provides a universal tool for probing the dynamical origins of spherically symmetric spacetimes.

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.