Hawking (1988: 88-9):
The work that Roger Penrose and I did between 1965 and 1970 showed that, according to general relativity, there must be a singularity of infinite density and space-time curvature within a black hole. This is rather like the big bang at the beginning of time, only it would be an end of time for the collapsing body and the astronaut. At this singularity the laws of science and our ability to predict the future would break down.
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From the perspective of Systemic Functional Linguistic Theory, according to the General Theory of Relativity, a singularity is a geometric point at which intervals of the three spatial dimensions contract to 0 and time intervals expand to ∞ due to the presence of matter. Curvature is a feature of particle trajectories through regions of contracted space intervals.
The singularity of a black hole and the singularity of the Big Bang differ significantly in the fact that the former is located in space and surrounded by matter-energy, whereas the latter is not, since it represents the space of the entire universe as a geometric point.
If time is the dimension measuring the unfolding of processes, the end of time is the end of all processes whose unfolding time measures. At a singularity, there are no spatial dimensions for processes to unfold in, and no space for the quantum fields in which particles are probabilistically instantiated.
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