Extended time-travelling objects in Misner space

Misner space is a two-dimensional (2D) locally-flat spacetime which elegantly demonstrates the emergence of closed timelike curves from causally well-behaved initial conditions. Here we explore the motion of rigid extended objects in this time-machine spacetime. This kind of 2D time-travel is found to be risky due to inevitable self-collisions (i.e. collisions of the object with itself). However, in a straightforward four-dimensional generalization of Misner space (a physically more relevant spacetime obviously), we find a wide range of "safe" time-travel orbits free of any self-collisions.