The Cauchy problem for the scalar wave equation is well defined on a class of spacetimes with closed timelike curves

We study the massless scalar wave equation on a class of asymptotically flat, static spacetimes with closed timelike curves (CTC’s), in which all future-directed CTC’s traverse one end of a handle (wormhole) and emerge from the other end at an earlier time. Existence of smooth, asymptotically regular solutions is proved for smooth data with finite energy given in ${\mathit{scrI}}^{\mathrm{-}}$. The proof requires a generalized spectral decomposition for a non-Hermitian operator. We also prove that this solution is unique among solutions that die off in time.