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International Journal of Theoretical Physics

, Volume 30, Issue 4, pp 555–565 | Cite as

Cauchy boundary andb-incompleteness of space-time

  • Jacek Gruszczak
  • Michael Heller
  • Zdzisław Pogoda
Article

Abstract

It is shown that if a space-time (M, g) is time-orientable and its Levi-Civita connection [in the bundle of orthonormal frames over (M, g)] is reducible to anO(3) structure, one can naturally select a nonvanishing timelike vector fieldξ and a Riemann metricg+ onM. The Cauchy boundary of the Riemann space (M, g+) consists of “endpoints” ofb-incomplete curves in (M, g); we call it theCauchy singular boundary. We use the space-time of a cosmic string with a conic singularity to test our method. The Cauchy singular boundary of this space-time is explicitly constructed. It turns out to consist of what should be expected.

Keywords

Endpoint Field Theory Elementary Particle Quantum Field Theory Cosmic String 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • Jacek Gruszczak
    • 1
    • 2
  • Michael Heller
    • 3
    • 2
  • Zdzisław Pogoda
    • 4
  1. 1.Institute of PhysicsPedagogical UniversityCracowPoland
  2. 2.Cracow Group of CosmologyPoland
  3. 3.Vatican Astronomical ObservatoryVatican City State
  4. 4.Institute of MathematicsJagiellonian UniversityCracowPoland

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