Birkhoff's Theorem and Uniqueness: A Peek Beyond General Relativity
arXiv:2411.09193 · doi:10.1016/j.physletb.2025.139974
Abstract
In General Relativity, Birkhoff's theorem asserts that any spherically symmetric vacuum solution must be static and asymptotically flat. In this paper, we study the validity of Birkhoff's theorem for a broad class of modified gravity theories in four spacetime dimensions, including quadratic and higher-order gravity models. We demonstrate that the Schwarzschild spacetime remains the unique Einstein branch solution outside any spherically symmetric configuration of these theories. Consequently, unlike black holes, the breakdown of junction conditions at the surface of the star further implies that the actual spacetime metric outside a horizonless star in these modified theories cannot simultaneously be spherically symmetric and remain within the Einstein branch. This insight offers a unique observational probe for theories beyond General Relativity.
Accepted in Physics Letters B: 8 pages, no figure
References in corpus (42)
- Observation of Gravitational Waves from a Binary Black Hole Merger
- The Cosmological Constant and Dark Energy
- Particle Dark Matter: Evidence, Candidates and Constraints
- Modified Gravity and Cosmology
- The Confrontation between General Relativity and Experiment
- Tests of general relativity with GW150914
- Testing General Relativity with Present and Future Astrophysical Observations
- Tests of General Relativity with Binary Black Holes from the second LIGO-Virgo Gravitational-Wave Transient Catalog
- Black holes, gravitational waves and fundamental physics: a roadmap
- Open data from the third observing run of LIGO, Virgo, KAGRA and GEO
- Black Holes in Higher-Derivative Gravity
- A new cubic theory of gravity in five dimensions: Black hole, Birkhoff's theorem and C-function
- Spherically Symmetric Solutions in Higher-Derivative Gravity
- Physical non-equivalence of the Jordan and Einstein frames
- Shortcuts to high symmetry solutions in gravitational theories
- Review of the Advanced LIGO gravitational wave observatories leading to observing run four
- Non-Schwarzschild black-hole metric in four dimensional higher derivative gravity: analytical approximation
- Birkhoff's theorem in Lovelock gravity
- Quintic quasi-topological gravity
- The Jebsen-Birkhoff theorem in alternative gravity
- Birkhoff's Theorem for Three-Dimensional AdS Gravity
- Transformations between Jordan and Einstein frames: Bounces, antigravity, and crossing singularities
- Birkhoff's Theorem in Higher Derivative Theories of Gravity
- A simple proof of Birkhoff's theorem for cosmological constant
- Lichnerowicz Modes and Black Hole Families in Ricci Quadratic Gravity
- Black holes and other exact spherical solutions in Quadratic Gravity
- Birkhoff for Lovelock Redux
- Exact solutions to quadratic gravity
- Scalar-tensor representation of gravity and Birkhoff's theorem
- Almost Birkhoff Theorem in General Relativity
- Instability of spherically-symmetric black holes in Quadratic Gravity
- Jebsen-Birkhoff theorem and its stability in f(R) gravity
- Black Hole Zeroth Law in Higher Curvature Gravity
- Probing Quadratic Gravity with the Event Horizon Telescope
- Nonlinear Evolution of Quadratic Gravity in 3+1 Dimensions
- Birkhoff Theorem and Matter
- The zeroth law of black hole thermodynamics in arbitrary higher derivative theories of gravity
- Infinitely degenerate exact Ricci-flat solutions in f(R) gravity
- On Birkhoff's Theorem in Horava Gravity
- On the validity of the 5-dimensional Birkhoff theorem: The tale of an exceptional case
- Topical Collection: Testing the Kerr spacetime with gravitational-wave and electromagnetic observations
- Is Birkhoff's Theorem Valid in Einstein-Aether Theory?