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Space-Time Singularities and Raychaudhuri Equations

Author

Listed:
  • Mohajan, Haradhan

Abstract

Raychaudhuri equations play important roles to describe the gravitational focusing and space-time singularities. Amal Kumar Raychaudhuri established it in 1955 to describe gravitational focusing properties in cosmology. When the star is heavier than a few solar masses, it could undergo an endless gravitational collapse without achieving any equilibrium state. The final outcome of gravitational collapse of a massive star must necessarily be a black hole which covers the resulting space-time singularity and causal message from the singularity cannot reach the external observer at infinity. In this article Raychaudhuri equations are derived with the help of general relativity and topological properties. An attempt has been taken here to describe gravitational focusing and space-time singularities in some detail with easier mathematical calculations.

Suggested Citation

  • Mohajan, Haradhan, 2013. "Space-Time Singularities and Raychaudhuri Equations," MPRA Paper 54069, University Library of Munich, Germany, revised 10 Aug 2013.
    • Handle: RePEc:pra:mprapa:54069
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    File URL: https://mpra.ub.uni-muenchen.de/54069/1/MPRA_paper_54069.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.
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    Cited by:

    1. 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.
    2. Mohajan, Haradhan, 2016. "Singularities in Global Hyperbolic Space-time Manifold," MPRA Paper 82953, University Library of Munich, Germany, revised 16 Mar 2016.

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    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, Haradhan, 2014. "Gravitational Collapse of a Massive Star and Black Hole Formation," MPRA Paper 83188, University Library of Munich, Germany, revised 10 Aug 2014.
    3. Mohajan, Haradhan, 2013. "General upper limit of the age of the Universe," MPRA Paper 53711, University Library of Munich, Germany, revised 04 Dec 2013.
    4. 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.
    5. Mohajan, Haradhan, 2013. "Minkowski geometry and space-time manifold in relativity," MPRA Paper 51627, University Library of Munich, Germany, revised 03 Nov 2013.
    6. Mohajan, Haradhan, 2016. "Global Hyperbolicity in Space-Time Manifold," MPRA Paper 83036, University Library of Munich, Germany, revised 14 Mar 2016.

    More about this item

    Keywords

    Gravitational focusing; Raychaudhuri equations; singularities.;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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