Birkhoff's Theorem for Three-Dimensional AdS Gravity

Abstract

All three-dimensional matter-free spacetimes with negative cosmological constant, compatible with cyclic symmetry are identified. The only cyclic solutions are the 2+1 (BTZ) black hole with SO(2) x R isometry, and the self-dual Coussaert-Henneaux spacetimes, with isometry groups SO(2) x SO(2,1) or SO(2) x SO(2).

11 pages, RevTeX4; minor typos corrected, Ref. added, accepted for publication in Phys. Rev. D

References in corpus (3)

• Nariai, Bertotti-Robinson and anti-Nariai solutions in higher dimensions
• Quotients of AdS_{p+1} x S^q: causally well-behaved spaces and black holes
• Quotients of anti-de Sitter space

Cited by in corpus (34)

• Stealth Scalar Field Overflying a 2+1 Black Hole
• A simple proof of Birkhoff's theorem for cosmological constant
• Nonlinear extensions of gravitating dyons: from NUT wormholes to Taub-Bolt instantons
• Extremal limit for charged and rotating 2+1-dimensional black holes and Bertotti-Robinson geometry
• (Super-)renormalizably dressed black holes
• Dynamical formation and evolution of (2+1)-dimensional charged black holes
• Hawking-Ellis classification of stress-energy: test-fields versus back-reaction
• The tetralogy of Birkhoff theorems
• Gravity/CFT correspondence for three dimensional Einstein gravity with a conformal scalar field
• No hair theorems for stationary axisymmetric black holes
• The Generalized Uncertainty Principle in f(R) Gravity for a Charged Black Hole
• Outer Entropy and Quasilocal Energy
• Phase transitions of black strings in dynamical Chern-Simons modified gravity
• Contact Geometry in Superconductors and New Massive Gravity
• Overspinning naked singularities in AdS${}_3$ spacetime
• Notes on the Area Theorem
• Quantum backreaction for overspinning BTZ geometries
• Thurston Geometries in Three-Dimensional New Massive Gravity
• New black hole solutions in three-dimensional $f(R)$ gravity
• General properties and some solutions of generalized Einstein - Eddington affine gravity I
• Inside the BTZ black hole
• Adiabatic analysis of the rotating BTZ black hole
• Holevo Information of Black Hole Mesostates
• Birkhoff-like theorem for rotating stars in (2+1) dimensions
• Inhomogeneous metrics on complex bundles in Lovelock gravity
• Three dimensional stationary cyclic symmetric Einstein-Maxwell solutions; energy, mass, momentum, and algebraic tensors characteristics
• Noncritical M-theory: Three Dimensions
• Quasinormal modes of three $(2+1)$-dimensional black holes in string theory, conformal gravity, and Hu-Sawicki $F(R)$ theory via the Heun function
• The (2+1)-dim Axial Universes -- Solutions to the Einstein Equations, Dimensional Reduction Points, and Klein-Fock-Gordon Waves
• New Spacetimes for Rotating Dust in (2+1)-Dimensional General Relativity
• Birkhoff's Theorem and Uniqueness: A Peek Beyond General Relativity
• Non-Abelian black holes in conformal gravity
• Surveying the Three-Dimensional Fixed Points of T-Duality
• Regular $(2+1)$-dimensional spatially homogeneous ${\alpha }^{\prime }$-corrected BTZ-like black hole in string theory