Singularities exist in Black Holes from "summary" of A Brief History of Time by Stephen W. Hawking
When a massive star runs out of fuel, it can no longer support itself against its own gravitational pull. The star collapses under its own weight, forming a black hole - a region of space where gravity is so strong that nothing, not even light, can escape. The boundary surrounding a black hole is known as the event horizon. Anything that crosses the event horizon is doomed to fall into the black hole, never to return. At the center of a black hole lies a singularity, a point where the gravitational field becomes infinitely strong and space-time curves infinitely. The laws of physics as we know them break down at the singularity, making it a point of infinite density and zero volume. In other words, a singularity is a place where the known laws of physics cease to apply, and our current understandi...
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