  Gott recently has constructed a spacetime modeled by two infinitely long,
parallel cosmic strings which pass and gravitationally interact with each
other. For large enough velocity, the spacetime will contain closed timelike
curves. An explicit construction of the solution for a scalar field is
presented in detail and a proof for the existence of such a solution is given
for initial data satisfying conditions on an asymptotically null partial Cauchy
surface.
  Solutions to smooth operators on the covering space are invariant under the
isometry are shown to be pull back of solutions of the associated operator on
the base space.
  Projection maps and translation operators for the covering space are
developed for the spacetime, and explicit expressions for the projection
operator and the isometry group of the covering space are given. It is shown
that the Gott spacetime defined is a quotient space of Minkowski space by the
discrete isometry subgroup of self-equivalences of the projection map.
