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Singularities in Global Hyperbolic Space-time Manifold

Author

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  • Mohajan, Haradhan

Abstract

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. There are two types of singularities in the space-time manifold. First one is called the Big Bang singularity. This type of singularity must be interpreted as the catastrophic event from which the entire universe emerged, where all the known laws of physics and mathematics breakdown in such a way that we cannot know what was happened during and before the big bang singularity. The second type is Schwarzschild singularity, which is considered as the end state of the gravitational collapse of a massive star which has exhausted its nuclear fuel providing the pressure gradient against the inwards pull of gravity. Global hyperbolicity is the most important condition on causal structure space-time, which is involved in problems as cosmic censorship, predictability, etc. Here both types of singularities in global hyperbolic space-time manifold are discussed in some details.

Suggested Citation

  • Mohajan, Haradhan, 2016. "Singularities in Global Hyperbolic Space-time Manifold," MPRA Paper 82953, University Library of Munich, Germany, revised 16 Mar 2016.
    • Handle: RePEc:pra:mprapa:82953
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    File URL: https://mpra.ub.uni-muenchen.de/82953/1/MPRA_paper_82953.pdf
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    References listed on IDEAS

    as
    1. Mohajan, Haradhan, 2013. "Space-Time Singularities and Raychaudhuri Equations," MPRA Paper 54069, University Library of Munich, Germany, revised 10 Aug 2013.
    2. Mohajan, Haradhan, 2013. "Schwarzschild Geometry from Exact Solution of Einstein Equation," MPRA Paper 50795, University Library of Munich, Germany, revised 16 Oct 2013.
    3. Mohajan, Haradhan, 2016. "Global Hyperbolicity in Space-Time Manifold," MPRA Paper 83036, University Library of Munich, Germany, revised 14 Mar 2016.
    4. Mohajan, Haradhan, 2013. "Friedmann, Robertson-Walker (FRW) Models in Cosmology," MPRA Paper 52402, University Library of Munich, Germany, revised 20 Dec 2013.
    5. Mohajan, Haradhan, 2015. "Basic Concepts of Differential Geometry and Fibre Bundles," MPRA Paper 83002, University Library of Munich, Germany, revised 18 Feb 2015.
    6. Mohajan, Haradhan, 2013. "Upper Limit of the Age of the Universe with Cosmological Constant," MPRA Paper 55597, University Library of Munich, Germany, revised 19 Oct 2013.
    7. Mohajan, Haradhan, 2013. "General upper limit of the age of the Universe," MPRA Paper 53711, University Library of Munich, Germany, revised 04 Dec 2013.
    8. Mohajan, Haradhan, 2013. "Minkowski geometry and space-time manifold in relativity," MPRA Paper 51627, University Library of Munich, Germany, revised 03 Nov 2013.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. 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.
    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. "Sensitivity Analysis of Inputs of an Organization: A Profit Maximization Exploration," MPRA Paper 117121, University Library of Munich, Germany, revised 12 Mar 2023.
    5. 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.
    6. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Bulimia Nervosa: A Psychiatric Problem of Disorder," MPRA Paper 117258, University Library of Munich, Germany, revised 17 Mar 2023.

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    More about this item

    Keywords

    Big Bang; global hyperbolicity; manifold; FRW model; Schwarzschild solution; space-time singularities;
    All these keywords.

    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General

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