Singularity
The point where our description of gravity stops producing meaningful answers.
General relativity says the matter inside a black hole collapses to a point of infinite density. Infinity in a theory usually signals that the theory has been pushed past its range rather than that nature contains an infinity, and the singularity is the standard example: gravity is strong and the scale is tiny, which is exactly the regime where quantum mechanics and relativity are known to disagree. What is actually there requires a theory of quantum gravity that nobody has.
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What is Singularity?
The point where our description of gravity stops producing meaningful answers.
Why does it matter?
Infinity in a theory usually signals that the theory has been pushed past its range rather than that nature contains an infinity, and the singularity is the standard example: gravity is strong and the scale is tiny, which is exactly the regime where quantum mechanics and relativity are known to disagree. What is actually there requires a theory of quantum gravity that nobody has.