Singularities in Global Hyperbolic Space-time Manifold

Haradhan Kumar Mohajan

doi:10.18034/ajase.v5i1.65

Authors

Haradhan Kumar Mohajan Assistant Professor, Faculty of Business Studies, Premier University, Chittagong, BANGLADESH

Keywords:

Big Bang

global hyperbolicity

manifold

FRW model

Schwarzschild solution

space-time singularities

Abstract

If a space-time is timelike or null geodesically incomplete but cannot be embedded in a larger space-time, then we say that it has a singularity. There are two types of singularities in the space-time 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 space-time, which is involved in problems as cosmic censorship, predictability, etc. Here both types of singularities in global hyperbolic space-time manifold are discussed in some details.

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