Particles with spin in stationary flat spacetimes

TL;DR

This paper constructs and classifies stationary flat 3D Lorentzian spacetimes with singularities, analyzing their geometric and causality properties, especially in the context of (2+1)-gravity with particles having spin.

Contribution

It introduces a new class of stationary flat spacetimes with singularities derived from Euclidean surfaces, and classifies those that are globally hyperbolic, with applications to (2+1)-gravity.

Findings

Classified all globally hyperbolic stationary flat spacetimes with singularities.

Derived conditions on observers to prevent causality violations.

Analyzed the causality structure in models with particles with spin.

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.