The Global Problem of Time
  Time does not obviously appear amongst the coordinates on the constrained phase space of general relativity in the Hamiltonian formulation. Recent work in finite-dimensional models claims that topological obstructions generically make the global definition of time impossible. It is shown here that a time coordinate can be globally defined on a constrained phase space by patching together local time coordinates, just as coordinates are defined on topologically non-trivial manifolds. 
Arlen Anderson