Time-periodic universes
  In this letter we construct a new time-periodic solution of the vacuum Einstein's field equations whose Riemann curvature norm takes the infinity at some points. We show that this solution is intrinsically time-periodic and describes a time-periodic universe with the "black hole". New physical phenomena are investigated and new singularities are analyzed for this universal model. 
De-Xing Kong, Kefeng Liu and Ming Shen