General Relativity/What is a singularity?

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The notion of a singularity in general relativity refers to a region of space-time where the equations of physics break down and lose their predictive meaning as seen by some potential observer. One kind of a singularity would be where things become infinite. This definition is limited as there are solutions to Einstein's field equations where there are no infinite quantities and yet the physical description through the mathematics becomes undefined. There has been a great deal of work leading to just what a good definition of a singularity should be. One possible definition in general relativity is that it's a region of space-time in which timelike curves cannot be extended to all of the spacetime. In effect singularities are unphysical and indicate the breakdown of the theory.