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Theoretical and Mathematical Physics

, Volume 157, Issue 3, pp 1646–1654 | Cite as

Cauchy problem on non-globally hyperbolic space-times

  • I. Ya. Aref’eva
  • T. Ishiwatari
  • I. V. Volovich
Article

Abstract

We consider solutions of the Cauchy problem for hyperbolic equations on non-globally hyperbolic space-times containing closed timelike curves (time machines). We prove that for the wave equation on such space-times, there exists a solution of the Cauchy problem that is discontinuous and in some sense unique for arbitrary initial conditions given on a hypersurface at a time preceding the formation of closed timelike curves. If the hypersurface of initial conditions intersects the region containing closed timelike curves, then the solution of the Cauchy problem exists only for initial conditions satisfying a certain self-consistency requirement.

Keywords

Cauchy problem non-globally hyperbolic space-time closed timelike curve 

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Copyright information

© MAIK/Nauka 2008

Authors and Affiliations

  • I. Ya. Aref’eva
    • 1
  • T. Ishiwatari
    • 1
  • I. V. Volovich
    • 1
  1. 1.Steklov Mathematical InstituteRASMoscowRussia

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