Cauchy Problem on Non-globally Hyperbolic Spacetimes

Understand

Solutions of the Cauchy problem for the wave equation on a non-globally hyperbolic spacetime, which contains closed timelike curves (time machines) are considered.

• It is proved, that there exists a solution of the Cauchy problem, it is discontinuous and in some sense unique for arbitrary initial conditions, which are given on a hypersurface at time, that precedes the formation of closed timelike curves (CTC).
• If the hypersurface of initial conditions intersects the region containing CTC, then the solution of the Cauchy problem exists only for such initial conditions, that satisfy a certain requirement of self-consistency.