2000/12/05 by Ingemar Bengtsson, Johan Brännlund, Johan Braennlund
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Geodesic #Group (periodic table) #Homotopy and Cohomology in Algebraic Topology #Hyperbolic equilibrium point #Modular design #Modular group #Noncommutative and Quantum Gravity Theories #Point (geometry) #Space (punctuation) #Topology (electrical circuits) #Torus #gr-qc
paper · pdf · doi:10.1063/1.1378302
published in Journal of Mathematical Physics 42(8), 3565-3579 (American Institute of Physics)
arxiv created 2000/12/05 · openalex publication_date 2001/08/01 · arxiv updated 2015/06/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
2+1 gravity for space–times with topology R×T2 has been much studied. We add a description of how to extend these space–times across a Cauchy horizon into a region where the torus becomes Lorentzian. The result is a one parameter family of tori given by a geodesic in the “Teichmüller space” of Lorentzian tori. We describe this in detail. We also point out that if the modular group is regarded as part of the gauge group then these space–times offer a nice toy model for the dynamics of Bianchi IX models; in the region where the tori are spacelike the dynamics is described exactly by a hyperbolic billiard. On the other hand the modular group acts ergodically on the Teichmüller space of Lorentzian tori.