 General relativity, Einstein's theory of space, time, and gravity, allows for the existence of singularities. Everyone agrees on this. When it comes to the question of how, precisely, singularities are to be defined, however, there is widespread disagreement. Singularities in some way signal a breakdown of the geometry of spacetime itself, but this presents an obvious difficulty in referring to a singularity as a “thing” that resides at some location in spacetime: without a well-behaved geometry, there can be no location. For this reason, some philosophers and physicists have suggested that we should not speak of “singularities” at all, but rather of “singular spacetimes”. In this entry, the two formulations will generally be treated as equivalent, but the distinction will be highlighted when it becomes significant. 