Particles with spin in stationary flat spacetimes |
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Authors: | Thierry Barbot Catherine Meusburger |
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Institution: | 1. Laboratoire d??Analyse Non Lin??aire et G??om??trie, Universit?? d??Avignon et des pays de Vaucluse, 33, Rue Louis Pasteur, 84 018, Avignon, France 2. Department Mathematik, FAU Erlangen-N??rnberg, Cauerstrasse 11, 91058, Erlangen, Germany
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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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