Particles with spin in stationary flat spacetimes

Details Particles with spin in stationary flat spacetimes Particles with spin in stationary flat spacetimes

2011-08-04

arxiv.org/abs/1108.1005v2

Mathematics

Differential Geometry

27 pages, 6 figures, references and explanations added

Scientific paper

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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