Pure radiation metric with stable closed timelike curves

Abstract

Here we present an example of an axially symmetric spacetime, representing pure radiation, and admitting circular closed timelike curves (CTCs) on the \(z= \hbox {constant plane}\). The spacetime is regular everywhere, having no curvature singularities and is locally isometric to (non-vacuum) pp wave spacetimes. The stability of the CTCs under linear perturbations is studied and they are found to be stable from a calculation of the Lyapunov exponent for the deviation vector. We also demonstrate that the spacetime also admits non-circular CTCs which do not lie in this plane. A modification of the metric is also studied and we find that a region of this spacetime behaves like a time-machine where CTCs appear after a certain instant of time.