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This article is cited in 8 scientific papers (total in 8 papers)
Cauchy problem on non-globally hyperbolic space-times
I. Ya. Aref'eva, I. V. Volovich, T. Ishiwatari Steklov Mathematical Institute, Russian Academy of Sciences
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.
Received: 23.06.2008
Citation:
I. Ya. Aref'eva, I. V. Volovich, T. Ishiwatari, “Cauchy problem on non-globally hyperbolic space-times”, TMF, 157:3 (2008), 334–344; Theoret. and Math. Phys., 157:3 (2008), 1646–1654
Linking options:
https://www.mathnet.ru/eng/tmf6283https://doi.org/10.4213/tmf6283 https://www.mathnet.ru/eng/tmf/v157/i3/p334
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