Cauchy boundary andb-incompleteness of space-time |
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Authors: | Jacek Gruszczak Michael Heller Zdzis?aw Pogoda |
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Institution: | (1) Institute of Physics, Pedagogical University, ul. Podchoraych 2, 30-084 Cracow, Poland;(2) Cracow Group of Cosmology, Poland;(3) Vatican Astronomical Observatory, V-00120, Vatican City State;(4) Institute of Mathematics, Jagiellonian University, ul. Reymonta 4, 30-059 Cracow, Poland |
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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 field 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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