Birkhoff’s theorem for three-dimensional AdS gravity

2004/03/31 by Eloy Ayón-Beato, Eloy Ayón–Beato, Cristián Martínez +1 · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Geodesy #Geology #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #gr-qc #hep-th

paper · pdf · doi:10.1103/physrevd.70.044027

published as Phys.Rev. D70 (2004) 044027 · 11 pages, RevTeX4; minor typos corrected, Ref. added, accepted for publication in Phys. Rev. D

arxiv created 2004/06/03 · openalex publication_date 2004/08/20 · arxiv updated 2016/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

All three-dimensional matter-free space-times with negative cosmological constant, compatible with cyclic symmetry, are identified. The only cyclic solutions are the 2+1 (BTZ) black hole with SO(2)\ifmmode×\else\texttimes\fiR isometry, and the self-dual Coussaert-Henneaux space-times, with isometry groups SO(2)\ifmmode×\else\texttimes\fiSO(2,1) or SO(2)\ifmmode×\else\texttimes\fiSO(2).

Citations

• Quantum Gravity in 2+1 Dimensions
• Black hole in three-dimensional spacetime
• The Large Scale Structure of Space-Time
• Geometry of the 2+1 Black Hole

Cited by

• Stealth scalar field overflying a 2+1 black hole