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"The theory of general relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole".

Why does this happen? I mean, why something finite (like the core of a very masive star) should lead to an infinitly small point (singularity). For me it's like spacetime has a "wekness" and it breaks if a region contains to much mass/energy.

I imagined that the matter will just be very very compacted, but not infinitly compacted and the spacetime bent accordingly.

Neutron stars are also very compacted and they bend a lot the space time.

I don't understand why if we continue to compress the matter even more (and I don't say "compress it to an infinitly small point"), suddenly the black hole is created. Why is this happening?

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The further you compress a body of matter (making it denser), the greater the surface gravity becomes- and gravity is a distortion of spacetime. As the surface gravity goes up, the spacetime distortion becomes more extreme and the escape velocity for a projectile fired upwards from that surface gets bigger and bigger. At some point, the spacetime distortion is so great that the escape velocity equals the speed of light and this is when it is usually said that a black hole forms. For very large things like stars, the compression is performed by gravity.

As to what is actually going on inside a black hole as it forms, we have mathematical models of the process but no way to extract data from a real black hole to determine if our models are correct or not.

Note also that what we can see and learn about a black hole depends on whether we are observing it from outside or whether we are freely falling into it. This greatly complicates the problem of understanding what sort of thing a black hole really is.

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