Closed timelike curves produced by pairs of moving cosmic strings: Exact solutions

Exact solutions of Einstein’s field equations are presented for the general case of two moving straight cosmic strings that do not intersect. The solutions for parallel cosmic strings moving in opposite directions, each with ${\gamma }_{\mathit{s}}$>(sin4πμ${)}^{\mathrm{-}1}$ in the laboratory frame show closed timelike curves (CTC’s) that circle the two strings as they pass, allowing observers to visit their own past. Similar results occur for nonparallel strings, and for masses in (2+1)-dimensional spacetime. For finite string loops the possibility that black-hole formation may prevent the formation of CTC’s is discussed.