Mohajan, Haradhan (2016): Global Hyperbolicity in SpaceTime Manifold. Published in: International Journal of Professional Studies , Vol. 1, No. 1 (30 June 2016): pp. 1430.

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Abstract
Global hyperbolicity is the most important condition on causal structure spacetime, which is involved in problems as cosmic censorship, predictability etc. An open set O is said to be globally hyperbolic if, i) for every pair of points x and y in O the intersection of the future of x and the past of y has compact closure i.e., a spacetime is said to be globally hyperbolic if the sets are compact for all (i.e., no naked singularity can exist in spacetime topology), and ii) strong causality holds on O i.e., there are no closed or almost closed time like curves contained in O. Here is causal future and is the causal past of an event x. If a spacetime is timelike or null geodesically incomplete but cannot be embedded in a larger spacetime then we say that it has a singularity. An attempt is taken here to discuss global hyperbolicity and spacetime singularity by introducing definitions, propositions and displaying diagrams appropriately.
Item Type:  MPRA Paper 

Original Title:  Global Hyperbolicity in SpaceTime Manifold 
English Title:  Global Hyperbolicity in SpaceTime Manifold 
Language:  English 
Keywords:  Cauchy surface, causality, global hyperbolicity, spacetime manifold, spacetime singularities. 
Subjects:  C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C30  General 
Item ID:  83036 
Depositing User:  Haradhan Kumar Mohajan 
Date Deposited:  01 Dec 2017 09:38 
Last Modified:  01 Dec 2017 09:39 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/83036 