Mohajan, Haradhan (2016): Singularities in Global Hyperbolic Spacetime Manifold. Published in: Asian Journal of Applied Science and Engineering , Vol. 1, No. 5 (26 March 2016): pp. 4158.

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Abstract
If a spacetime is timelike or null geodesically incomplete but cannot be embedded in a larger spacetime, then we say that it has a singularity. There are two types of singularities in the spacetime manifold. First one is called the Big Bang singularity. This type of singularity must be interpreted as the catastrophic event from which the entire universe emerged, where all the known laws of physics and mathematics breakdown in such a way that we cannot know what was happened during and before the big bang singularity. The second type is Schwarzschild singularity, which is considered as the end state of the gravitational collapse of a massive star which has exhausted its nuclear fuel providing the pressure gradient against the inwards pull of gravity. Global hyperbolicity is the most important condition on causal structure spacetime, which is involved in problems as cosmic censorship, predictability, etc. Here both types of singularities in global hyperbolic spacetime manifold are discussed in some details.
Item Type:  MPRA Paper 

Original Title:  Singularities in Global Hyperbolic Spacetime Manifold 
English Title:  Singularities in Global Hyperbolic Spacetime Manifold 
Language:  English 
Keywords:  Big Bang, global hyperbolicity, manifold, FRW model, Schwarzschild solution, spacetime singularities 
Subjects:  C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C20  General 
Item ID:  82953 
Depositing User:  Haradhan Kumar Mohajan 
Date Deposited:  29 Nov 2017 05:33 
Last Modified:  28 Sep 2019 01:45 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/82953 