When Time Emerges

We study the geodesics in a space-time where a metric with Minkowski type signature is continued across a singularity to a region with a different space-time signature. Contrary to naive expectation, the motion of test particles does not end up in a catastrophe. Depending on the form of the signature change and the initial conditions, timelike (or light-like) geodesics are either reflected at the singularity or even leave the Minkowski sector and use the region with the flipped metric for a time travel. An observer in the Minkowski sector interprets this as the creation of a particle and an antiparticle at the singularity.