Existence and uniqueness of classical solutions of the Cauchy problem on nonglobally hyperbolic manifolds

We consider the Cauchy problem for the wave equation on the Misner space, a nonglobally hyperbolic manifold with closed timelike lines. We prove that the existence and uniqueness of a classical solution are equivalent to self-consistency conditions much more rigorous than a finite collection of pointlike conditions occurring in this problem on the Minkowski plane with an attached handle.