Space-Time Curvature Singularities in Classical Cosmology Due to Gravitational Collapse

Abstract

This article takes an attempt to analyze space-time singularity within the black hole region. If a star is weightier than the multiple times of mass of the sun, it might suffer a boundless gravitational collapse without attaining any stationary state. The ultimate result of gravitational collapse of a heavier star must essentially be a black hole. Consequently, space-time singularity must be secreted within the black hole area and pivotal message from the singularity cannot be reached to an observer who is uniting outside of black hole or may stay at infinity. This situation faces when the star has finished its internal nuclear fuel that is used to support the external pressure against the interior dragging gravitational forces. The Schwarzschild metric represents a static and stationary exact solution of the Einstein’s field equation. It has two singularities at r = 0 and at r = 2m, where r = 0 is a true physical singularity, and the event horizon r = 2m is an artificial singularity. The coordinate singularity at r = 2s can be removed by the use of Kruskal-Szekeres extension, and the genuine space-time singularity at r = 0 which is concealed within the event horizon at r < 2m cannot be removed anyway. Again in Friedmann, Robertson-Walker (FRW) model there presents an unavoidable curvature singularity at t = 0 which cannot be removed by any coordinate conversion. At this situation, the scale factor S(t) also disappears and all materials are crumpled to null size owing to endless gravitational tidal force. In this paper an effort has been arranged to discuss the curvature space-time singularities in some details.