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Singularity Theorems

Theorems developed by Stephen Hawking and Roger Penrose that quantify the specific conditions under which singularities are the inevitable result of solutions to General Relativity. These theorems demonstrate that in the framework of GR, every black hole must contain a singularity at its center, and all expanding universes like ours must have begun with a big bang singularity.

Hawking and Penrose have formulated singularity theorems using the Raychaudhury equation describing the divergence of a family of geodesic family (paths through curved space-time) for both the weak energy condition, in which the geodesic congruence must be null, and the strong energy condition in which the geodesic congruence is time-like.

Web Resources On Singularity Theorems

Singularity Theorems for Dummies: Avoiding the Wrath of Hawking and Penrose for the Rest of Us
A Non-Singular Universe
Penrose-Hawking singularity theorems (Wikipedia)

Book Resources On Singularity Theorems

The Nature of Space and Time by Stephen Hawking and Roger Penrose
Space and Time in Special Relativity by N. David Mermin.
Understanding Space-Time: The Philosophical Development of Physics from Newton to Einstein by Robert DiSalle

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