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Schwarzschild Geometry from Exact Solution of Einstein Equation


  • Mohajan, Haradhan


An exact solution of Einstein equation is easier than actual solution. The Schwarzschild metric is established on the basis of Einstein’s exact solution and it is also a static and stationary solution. The Schwarzschild solution expresses the geometry of a spherically symmetric massive body’s (star) exterior solution. It predicts small observable departures from the Newtonian gravity. It also represents theory of black holes when sufficiently massive stars unable to support themselves against the pull of self gravity and must undergo a complete gravitational collapse when they have exhausted their internal nuclear fuel. Various sides of Schwarzschild geometry, such as, Kruskal–Szekeres extension, space-time singularities and black hole formation, are discussed with simple but detail calculations. The black hole is a region from which no causal signals can reach to the external observers and it contains a space-time singularity hidden within the event horizon.

Suggested Citation

  • Mohajan, Haradhan, 2013. "Schwarzschild Geometry from Exact Solution of Einstein Equation," MPRA Paper 50795, University Library of Munich, Germany, revised 16 Oct 2013.
  • Handle: RePEc:pra:mprapa:50795

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    Cited by:

    1. Mohajan, Haradhan, 2016. "Global Hyperbolicity in Space-Time Manifold," MPRA Paper 83036, University Library of Munich, Germany, revised 14 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. "Minkowski geometry and space-time manifold in relativity," MPRA Paper 51627, University Library of Munich, Germany, revised 03 Nov 2013.
    4. Mohajan, Haradhan, 2016. "Singularities in Global Hyperbolic Space-time Manifold," MPRA Paper 82953, University Library of Munich, Germany, revised 16 Mar 2016.
    5. 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.
    6. Mohajan, Haradhan, 2013. "Space-Time Singularities and Raychaudhuri Equations," MPRA Paper 54069, University Library of Munich, Germany, revised 10 Aug 2013.

    More about this item


    Einstein equation; Schwarzschild solution; Black hole; Space-time singularity.;

    JEL classification:

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

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