Gravitational singularity

A boundary or region of spacetime where classical general relativity breaks down, often indicated by incomplete paths of freely falling observers or divergent curvature.

Geodesic incompleteness: The failure of some geodesics to extend indefinitely within a spacetime. It is the central, coordinate-independent criterion used by singularity theorems.
Spacetime: The four-dimensional structure combining space and time in relativistic physics. A singularity concerns the limits of spacetime geometry, not merely matter compressed into a point.
Schwarzschild singularity: The central curvature singularity in the vacuum Schwarzschild solution for a nonrotating spherical mass. It is the standard black-hole example of a genuine curvature singularity.
Event horizon: A boundary beyond which events cannot send signals to distant observers. A horizon can hide a singularity but is not itself a singularity.
Curvature singularity: A singularity indicated by curvature quantities that diverge along some path. Diverging curvature is a familiar signal, though not the definition of every singularity.
General relativity: Einstein’s theory describing gravity as the curvature of spacetime. The breakdown at issue is specifically a limit of this classical theory.
Big Bang: The early hot, dense phase from which the observable universe expanded. Classical cosmological models trace past-directed paths toward a singular boundary associated with the Big Bang.
Cosmic censorship hypothesis: The conjecture that gravitational collapse generically hides singularities behind event horizons. It addresses whether singularities can be visible, not whether they form.
Einstein field equations: Differential equations relating spacetime curvature to the distribution of matter and energy. Their classical solutions produce the spacetimes in which singularity behavior is analyzed.
Geodesic: A path that locally extremizes distance or proper time in a curved spacetime. Incomplete freely falling geodesics provide a principal way to identify singular spacetimes.

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