Mohajan, Haradhan (2013): Schwarzschild Geometry from Exact Solution of Einstein Equation. Published in: Journal of Environmental Treatment Techniques , Vol. 1, No. 2 (18 October 2013)

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Abstract
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, spacetime 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 spacetime singularity hidden within the event horizon.
Item Type:  MPRA Paper 

Original Title:  Schwarzschild Geometry from Exact Solution of Einstein Equation 
English Title:  Schwarzschild Geometry from Exact Solution of Einstein Equation 
Language:  English 
Keywords:  Einstein equation, Schwarzschild solution, Black hole, Spacetime singularity. 
Subjects:  C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods 
Item ID:  50795 
Depositing User:  Haradhan Kumar Mohajan 
Date Deposited:  19 Oct 2013 18:01 
Last Modified:  30 Sep 2019 15:50 
References:  1 Hawking S.W., Ellis, G.F.R., The Large Scale Structure of Spacetime, Cambridge University Press, Cambridge. 1973. 2 Joshi P.S., Global Aspects in Gravitation and Cosmology, Clarendon Press, Oxford. 1993. 3 Joshi P.S., Kozameh C.N., Newman, E.T., Light Cone Cuts of Null Infinity in Schwarzschild Geometry, Journal of Mathematical Physics, 1983. 24(10): 2490–2497. 4 Kruskal, M.D., Maximal Extension of Schwarzschild Metric, Physical Review, 1960.119: 1743. 5 Mohajan H.K., Singularity Theorems in General Relativity, M. Phil. Dissertation, Lambert Academic Publishing, Germany. 2013. 6 Szekeres, P., On the Singularities of a Riemannian Manifold, Publ. Math. Debrecen. 1960. 7: 285. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/50795 