Cylindrical symmetry locally isometric $AdS_{4}$ spacetime
  We present a maximally symmetric vacuum spacetime, which is locally isometric anti- de Sitter, admitting closed timelike curves appear after a definite instant of time i.e., a time-machine spacetime. The spacetime is regular, free-from curvature singularities and an $4D$ extension of the Misner space in curved spacetime with identical causality violating properties. 
Faizuddin Ahmed, Davood Momeni, Debojit Sarma, Bidyut Bikash Hazarika,   Ratbay Myrzakulov
gr-qc