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

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

Jan 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991phrvl..66..401f&link_type=abstract

Physical Review Letters, Volume 66, Issue 4, January 28, 1991, pp.401-404

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40

Fundamental Problems And General Formalism, Exact Solutions

Scientific paper

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 scrI-. 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.

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