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Schwarzschild Geometry from Exact Solution of Einstein Equation

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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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.

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