Abstract
We construct stationary flat three-dimensional Lorentzian manifolds with singularities that are obtained from Euclidean surfaces with cone singularities and closed one-forms on these surfaces. In the application to (2 + 1)-gravity, these spacetimes correspond to models containing massive particles with spin. We analyse their geometrical properties, introduce a generalised notion of global hyperbolicity and classify all stationary flat spacetimes with singularities that are globally hyperbolic in that sense. We then apply our results to (2 + 1)-gravity and analyse the causality structure of these spacetimes in terms of measurements by observers. In particular, we derive a condition on observers that excludes causality violating light signals despite the presence of closed timelike curves in these spacetimes.
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T. Barbot was partially supported by CNRS, ANR GEODYCOS and A.N.R. program “Extensions of Teichmueller-Thurston theories (ETTT)”, ANR-09-BLAN-0116-01. C. Meusburger’s work is supported by the Emmy-Noether fellowship ME 3425/1-1 of the German Research Foundation (DFG). Research visits during which work on this project was undertaken were also supported by the Emmy-Noether fellowship ME 3425/1-1.
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Barbot, T., Meusburger, C. Particles with spin in stationary flat spacetimes. Geom Dedicata 161, 23–50 (2012). https://doi.org/10.1007/s10711-011-9692-y
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DOI: https://doi.org/10.1007/s10711-011-9692-y
Keywords
- Minkowski space
- Flat spacetime
- Global hyperbolicity
- Particle with spin
- Euclidean surface
- Cone singularity