Geometriae Dedicata

, Volume 161, Issue 1, pp 23–50 | Cite as

Particles with spin in stationary flat spacetimes

  • Thierry BarbotEmail author
  • Catherine Meusburger
Original 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.


Minkowski space Flat spacetime Global hyperbolicity Particle with spin Euclidean surface Cone singularity 

Mathematics Subject Classification (1991)

83C80 (83C57) 57S25 


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© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Laboratoire d’Analyse Non Linéaire et GéométrieUniversité d’Avignon et des pays de VaucluseAvignonFrance
  2. 2.Department MathematikFAU Erlangen-NürnbergErlangenGermany

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