Singularity (or Gravitational Singularity):
A region of space where the density of matter, or the curvature of spacetime, becomes infinite and the concepts of space and time cease to have any meaning. At this point, the whole fabric of spacetime ruptures and the precepts of Einstein’s General Theory of Relativity (and physics in general) break down and no longer apply, similar to the way in which a calculator returns an error when asked to divide by zero. According to general relativity, the Big Bang started with a singularity, and there is a singularity at the centre of a black hole.
SpaceTime:
Spacetime (or spacetime or the spacetime continuum) is any mathematical model that combines space and time into a single construct. The fourth dimension of time is traditionally considered to be of a different sort than the three dimensions of space in that it can only go forwards and not back but, in Albert Einstein’s General Theory of Relativity, space and time are seen to be essentially the same thing and can therefore be treated as a single entity.
