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Scope of Raychaudhuri equation in cosmological gravitational focusing and space-time singularities


  • Mohajan, Haradhan


Indian scientist Amal Kumar Raychaudhuri established ‘Raychaudhuri equation’ in 1955 to describe gravitational focusing properties in cosmology. This equation is extensively used in general relativity, quantum field theory, string theory and the theory of relativistic membranes. This paper investigates the issue of the final fate of a gravitationally collapsing massive star and the associated cosmic censorship problems and space-time singularities therein with the help of Raychaudhuri equation. It is conjecture that the universe is emerged from a big bang singularity where all the known laws of physics break down. On the other hand, when the star is heavier than a few solar masses, it could undergo an endless gravitational collapse without achieving any equilibrium state. This happens when the star has exhausted its internal nuclear fuel which provides the outwards pressure against the inwards pulling gravitational forces. Then for a wide range of initial data, a space-time singularity must develop. It is conjecture that such a singularity of gravitational collapse from a regular initial surface must always be hidden behind the event horizon of gravity; this is called the cosmic censorship hypothesis. Thus cosmic censorship implies that the final outcome of gravitational collapse of a massive star must necessarily be a black hole which covers the resulting space-time singularity. So, causal message from the singularity cannot reach the external observer at infinity. Raychaudhuri equation plays a pioneer role in cosmology to describe the gravitational focusing and space-time singularities.

Suggested Citation

  • Mohajan, Haradhan, 2013. "Scope of Raychaudhuri equation in cosmological gravitational focusing and space-time singularities," MPRA Paper 52544, University Library of Munich, Germany, revised 10 Dec 2013.
  • Handle: RePEc:pra:mprapa:52544

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    References listed on IDEAS

    1. Freeman, Alan, 2003. "When Things Go Wrong: the Political Economy of Market Breakdown," MPRA Paper 5586, University Library of Munich, Germany.
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    3. Harvey, David, 2005. "The New Imperialism," OUP Catalogue, Oxford University Press, number 9780199278084, June.
    4. Lant Pritchett, 1997. "Divergence, Big Time," Journal of Economic Perspectives, American Economic Association, vol. 11(3), pages 3-17, Summer.
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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.

    More about this item


    Cosmic censorship; Einstein equation; gravitational focusing; Raychaudhuri equation; singularities.;

    JEL classification:

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

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