Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2000-12-05
J.Math.Phys. 42 (2001) 3565-3579
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Scientific paper
2+1 gravity for spacetimes with topology RxT^2 has been much studied. We add a description of how to extend these spacetimes 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 "Teichmueller 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 spacetimes 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 Teichmueller space of Lorentzian tori.
Bengtsson Ingemar
Braennlund Johan
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