A new family of solutions to Einstein's vacuum field equations with cosmological constant

In this paper, we construct a new time-periodic solution and a new time-machine solution according to the general form of the new family of solutions to the Einstein's vacuum field equations with cosmological constant. The time-periodic solutions have some relations with the loop universe. The time-machine solutions are spacetime configurations including closed time-like curves (CTCs), and allowing physical observers to return to their own past. This problem has been of concern a lot recently. We expect the new solutions obtained in this paper can be applied in modern cosmology and general relativity.