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Cauchy boundary andb-incompleteness of space-time

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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.

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Gruszczak, J., Heller, M. & Pogoda, Z. Cauchy boundary andb-incompleteness of space-time. Int J Theor Phys 30, 555–565 (1991). https://doi.org/10.1007/BF00672901

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Keywords

  • Endpoint
  • Field Theory
  • Elementary Particle
  • Quantum Field Theory
  • Cosmic String