A simple proof of Birkhoff's theorem for cosmological constant
arXiv:0908.4110 · doi:10.1063/1.3503447
Abstract
We provide a simple, unified proof of Birkhoff's theorem for the vacuum and cosmological constant case, emphasizing its local nature. We discuss its implications for the maximal analytic extensions of Schwarzschild, Schwarzschild(-anti)-de Sitter and Nariai spacetimes. In particular, we note that the maximal analytic extensions of extremal and over-extremal Schwarzschild-de Sitter spacetimes exhibit no static region. Hence the common belief that Birkhoff's theorem implies staticity is false for the case of positive cosmological constant. Instead, the correct point of view is that generalized Birkhoff's theorems are local uniqueness theorems whose corollary is that locally spherically symmetric solutions of Einstein's equations exhibit an additional local killing vector field.
10 pages, 5 figures References added; typo in eqn. 12 fixed
References in corpus (9)
- Generalized Misner-Sharp quasi-local mass in Einstein-Gauss-Bonnet gravity
- Birkhoff's theorem in Lovelock gravity
- Birkhoff's Theorem for Three-Dimensional AdS Gravity
- Schwarzschild and Birkhoff a la Weyl
- Birkhoff for Lovelock Redux
- Modified gravity and the origin of inertia
- Maximally extended, explicit and regular coverings of the Schwarzschild - de Sitter vacua in arbitrary dimension
- Modified Gravity: living without Birkhoff I. DGP
- On the validity of the 5-dimensional Birkhoff theorem: The tale of an exceptional case
Cited by in corpus (32)
- The global non-linear stability of the Kerr-de Sitter family of black holes
- Thermodynamic ensembles with cosmological horizons
- Non-linear stability of the Kerr-Newman-de Sitter family of charged black holes
- Spherical inhomogeneous solutions of Einstein and scalar-tensor gravity: a map of the land
- The tetralogy of Birkhoff theorems
- Generalized Birkhoff theorem in the Poincaré gauge gravity theory
- Holographic Probes of Inner Horizons
- On the Static Spacetime of a Single Point Charge
- Local properties and global structure of McVittie spacetimes with non-flat FLRW backgrounds
- Black hole nonmodal linear stability: the Schwarzschild (A)dS cases
- IDEAL characterization of higher dimensional spherically symmetric black holes
- Light bending, static dark energy and related uniqueness of Schwarzschild-de Sitter spacetime
- Algebraic Properties of Einstein Solutions in Ghost-Free Bimetric Theory
- Midisuperspace foam and the cosmological constant
- Simultaneous baldness and cosmic baldness and Kottler spacetime
- A Holographic Description of Negative Energy States
- Relation between circular photon orbits and the stability of wormholes with the thin shell of a barotropic fluid
- Action Principle for Isotropic General Relativity
- Gauge invariant description of weak gravitational field on a spherically symmetric background with cosmological constant
- Newton gauge cosmological perturbations for static spherically symmetric modifications of the de Sitter metric
- Structural stability of spherical horizons
- Static and spherically symmetric vacuum spacetimes with non-expanding principal null directions in gravity
- Birkhoff's Theorem and Uniqueness: A Peek Beyond General Relativity
- On Birkhoff's theorem in ghost-free bimetric theory
- Extremal cosmological black holes in Horndeski gravity and the anti-evaporation regime
- Master Functions and Equations for Perturbations of Vacuum Spherically-Symmetric Spacetimes
- The curious case of the Buchdahl-Land-Sultana-Wyman-Ibañez-Sanz spacetime
- New time-dependent solutions of viable Horndeski gravity
- Embedding black holes and other inhomogeneities in the universe in various theories of gravity: a short review
- Dynamics of a nonminimally coupled scalar field in asymptotically spacetime
- Spacetime symmetries and geometric diffusion
- Gravity and its wonders: braneworlds and holography