Causality violation in plane wave spacetimes
  It is widely held that plane wave spacetimes are causally well behaved which means that they are free from causal pathologies such as closed timelike curves or closed null geodesics. In this paper, we show that one can get closed null geodesics in a plane wave metric by analytically solving the geodesic equations. 
Debojit Sarma, Mahadev Patgiri and Faiz Uddin Ahmed
gr-qc