The anti-de Sitter spacetime as a time machine

We construct an axially symmetric spacetime admitting, after a certain instant, closed timelike curves (CTCs) indicating that it is a time-machine spacetime. The spacetime, which is locally anti-de Sitter, is a four-dimensional extension of the Misner space with identical causality-violating properties. In this spacetime, CTCs evolve from a casually well-behaved initial hypersurface.