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Global Hyperbolicity in Space-Time Manifold

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  • Mohajan, Haradhan

Abstract

Global hyperbolicity is the most important condition on causal structure space-time, 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 space-time is said to be globally hyperbolic if the sets are compact for all (i.e., no naked singularity can exist in space-time 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 space-time is timelike or null geodesically incomplete but cannot be embedded in a larger space-time then we say that it has a singularity. An attempt is taken here to discuss global hyperbolicity and space-time singularity by introducing definitions, propositions and displaying diagrams appropriately.

Suggested Citation

  • Mohajan, Haradhan, 2016. "Global Hyperbolicity in Space-Time Manifold," MPRA Paper 83036, University Library of Munich, Germany, revised 14 Mar 2016.
  • Handle: RePEc:pra:mprapa:83036
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    File URL: https://mpra.ub.uni-muenchen.de/83036/1/MPRA_paper_83036.pdf
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    References listed on IDEAS

    as
    1. Mohajan, Haradhan, 2013. "Schwarzschild Geometry from Exact Solution of Einstein Equation," MPRA Paper 50795, University Library of Munich, Germany, revised 16 Oct 2013.
    2. Mohajan, Haradhan, 2013. "Friedmann, Robertson-Walker (FRW) Models in Cosmology," MPRA Paper 52402, University Library of Munich, Germany, revised 20 Dec 2013.
    3. Mohajan, Haradhan, 2015. "Basic Concepts of Differential Geometry and Fibre Bundles," MPRA Paper 83002, University Library of Munich, Germany, revised 18 Feb 2015.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Mohajan, Haradhan, 2016. "Singularities in Global Hyperbolic Space-time Manifold," MPRA Paper 82953, University Library of Munich, Germany, revised 16 Mar 2016.
    2. Mohajan, Devajit & Mohajan, Haradhan, 2023. "A Study on Nonlinear Budget Constraint of a Local Industrial Firm of Bangladesh: A Profit Maximization Investigation," MPRA Paper 117324, University Library of Munich, Germany, revised 27 Mar 2023.
    3. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Sensitivity Analysis for Utility Maximization: A Study on Lagrange Multipliers and Commodity Coupons," MPRA Paper 117077, University Library of Munich, Germany, revised 06 Jan 2023.
    4. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Glaserian Grounded Theory and Straussian Grounded Theory: Two Standard Qualitative Research Approaches in Social Science," MPRA Paper 117017, University Library of Munich, Germany, revised 20 Feb 2023.
    5. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Sensitivity Analysis of Inputs of an Organization: A Profit Maximization Exploration," MPRA Paper 117121, University Library of Munich, Germany, revised 12 Mar 2023.
    6. Mohajan, Devajit & Mohajan, Haradhan, 2023. "A Study on Body Fat Percentage for Physical Fitness and Prevention of Obesity: A Two Compartment Model," MPRA Paper 117158, University Library of Munich, Germany, revised Feb 2023.
    7. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Bulimia Nervosa: A Psychiatric Problem of Disorder," MPRA Paper 117258, University Library of Munich, Germany, revised 17 Mar 2023.
    8. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Sensitivity Analysis between Lagrange Multipliers and Consumer Budget: Utility Maximization Case," MPRA Paper 116907, University Library of Munich, Germany, revised 19 Feb 2023.
    9. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Mathematical Model for Nonlinear Budget Constraint: Economic Activities on Increased Budget," MPRA Paper 117299, University Library of Munich, Germany, revised 17 Mar 2023.
    10. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Long-Term Regular Exercise Increases V̇O2max for Cardiorespiratory Fitness," MPRA Paper 116962, University Library of Munich, Germany, revised 04 Feb 2023.

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    More about this item

    Keywords

    Cauchy surface; causality; global hyperbolicity; space-time manifold; space-time singularities.;
    All these keywords.

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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