Definition
A singularity is a point or region of spacetime where physical quantities — curvature, density, tidal forces — become formally infinite, and the equations of general relativity break down.
General relativity predicts two canonical singularities: at the centers of black holes, where gravitational collapse runs to completion, and at the Big Bang, where extrapolating cosmic expansion backward in time meets a point of zero size and infinite density.
Why it matters
How it works
The earliest known singular solution of Einstein's equations was the Schwarzschild metric (1916), with curvature diverging at r = 0. For decades many physicists hoped that real collapse would always be halted by something — pressure, rotation, asymmetries — before a singularity formed. The 1960s "singularity theorems" of Roger Penrose and Stephen Hawking ended that hope: under reasonable conditions on the matter content (positive energy density, in technical terms) and the existence of a "trapped surface," the formation of a singularity in the future is mathematically inevitable. Hawking applied an analogous argument running time backward to show that, under the same assumptions, the universe must have begun in a singularity.
A singularity is not a place inside spacetime — it is a boundary of the spacetime manifold. Some geodesics simply end there at finite proper time. The Schwarzschild singularity is a spacelike hypersurface in the future of every interior observer: like the moment "next Tuesday," it cannot be avoided by any future-directed motion. The Big Bang is similarly a spacelike past boundary of cosmological spacetime.
Most physicists view the predicted singularities as artifacts — places where general relativity is being asked questions it cannot answer. Energy densities approach the Planck scale (~10⁹⁶ kg/m³), where quantum-gravity effects must dominate. Candidate theories propose various resolutions: in loop quantum gravity, the Big Bang singularity is replaced by a "Big Bounce"; in string theory, extended-object behavior smears the point; in the no-boundary proposal of Hartle and Hawking (1983), the universe has no singular initial point at all when treated quantum-mechanically.