Cauchy problem in spacetimes with closed timelike curves

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Abstract
The laws of physics might permit the existence, in the real Universe, of closed timelike curves (CTC’s). Macroscopic CTC’s might be a semiclassical consequence of Planck-scale, quantum gravitational, Lorentzian foam, if such foam exists. If CTC’s are permitted, then the semiclassical laws of physics (the laws with gravity classical and other fields quantized or classical) should be augmented by a principle of self-consistency, which states that a local solution to the equations of physics can occur in the real Universe only if it can be extended to be part of a global solution, one which is well defined throughout the (nonsingular regions of) classical spacetime. The consequences of this principle are explored for the Cauchy problem of the evolution of a classical, massless scalar field Φ (satisfying □Φ=0) in several model spacetimes with CTC’s.

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