Some properties of time-machines

Closed time-like loops on space-time manifolds are discussed with a view to finding out whether time-machines exist. It is shown that a three-surface associated with causality violation, the 'time-machine boundary', has topology T2 x R1. This torus begins its existence as a singular closed null geodesic (C1), in agreement with a result due to Tipler (Phys. Rev.; D9:2203 (1974)). Null curves close to C1 carry off angular momentum to future null infinity, and it is calculated that this radiation process damps the rotation of a system to below the critical angular momentum at which causality violation occurs. (author)