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Part I

5. Singularity Theorems Prove a Model's Breakdown, Not a Physical Event

Penrose and Hawking's singularity theorems prove that under very general conditions, General Relativity's own equations must break down at a singularity. They do not prove that infinite density is a physical state nature actually reaches; a theorem about where a model's equations stop working is not the same as a theorem about what physically happens at that location. Reading the theorems as proof of a literal infinite-density event is an interpretive step the mathematics itself does not force [P26].

Source papers: P26

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