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Teoreticheskaya i Matematicheskaya Fizika, 2008, Volume 157, Number 3, Pages 334–344
DOI: https://doi.org/10.4213/tmf6283 (Mi tmf6283) 		 
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
Full-text PDF (490 kB) Citations (8)
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DOI: https://doi.org/10.4213/tmf6283
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
English version:
Theoretical and Mathematical Physics, 2008, Volume 157, Issue 3, Pages 1646–1654
DOI: https://doi.org/10.1007/s11232-008-0137-1
Bibliographic databases:
Document Type: Article
Language: Russian
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
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
    1. Bishop L.G., Costa F., Ralph T.C., “Time-Traveling Billiard-Ball Clocks: a Quantum Model”, Phys. Rev. A, 103:4 (2021), 042223  crossref  mathscinet  isi
    2. Osorio Morales J., Santillan O.P., “About the Cauchy Problem in Stelle'S Quadratic Gravity”, J. Cosmol. Astropart. Phys., 2019, no. 3, 026  crossref  mathscinet  isi  scopus
    3. Krasnikov S., “Back-in-Time and Faster-Than-Light Travel in General Relativity”, Back-in-Time and Faster-Than-Light Travel in General Relativity, Fundamental Theories of Physics, 193, Springer International Publishing Ag, 2018, 1–250  crossref  mathscinet  isi
    4. Arefeva I. Bagrov A. Saterskog P. Schalm K., “Holographic dual of a time machine”, Phys. Rev. D, 94:4 (2016), 044059  crossref  mathscinet  isi  elib  scopus
    5. O. V. Groshev, “Zadacha Koshi dlya volnovogo uravneniya na neglobalno giperbolicheskikh mnogoobraziyakh”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(22) (2011), 42–46  mathnet  crossref  elib
    6. Pavan A.B., Abdalla E., Molina C., “Stability, causality, and quasinormal modes of cosmic strings and cylinders”, Phys. Rev. D, 81:4 (2010), 044003, 10 pp.  crossref  adsnasa  isi  elib  scopus  scopus
    7. O. V. Groshev, “Existence and uniqueness of classical solutions of the Cauchy problem on nonglobally hyperbolic manifolds”, Theoret. and Math. Phys., 164:3 (2010), 1202–1207  mathnet  crossref  crossref  adsnasa  isi
    8. I. V. Volovich, O. V. Groshev, N. A. Gusev, E. A. Kuryanovich, “On Solutions to the Wave Equation on a Non-globally Hyperbolic Manifold”, Proc. Steklov Inst. Math., 265 (2009), 262–275  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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