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If it had infinite density, then would it not also have infinite gravity?

The word 'infinite' should be used with care. It is, essentially, a mathematical or philosophical notion and doesn't have a place in the real world. Serious Mathematicians don't even use the word without a load of qualifying statements.'Limitless' and 'vanishingly small' are less risky concepts.It is amazing that we brandish the word 'infinity' around on a daily basis when, in fact, it is one of the most difficult concepts around.QuoteIf it had infinite density, then would it not also have infinite gravity?It would be better to say that, as the radius approaches zero the gravitational field at the surface would get higher and higher without limit. Nothing has zero size.But, for someone at a fair distance away, the field would be the same, of course, whatever the radius. The 'inverse square law', when used casually, assumes a point mass - which is not really the case but allows you to do the sums accurately enough.

Since no one replied to my question, I'll elaborate. The situation with black holes is different from leptons like electrons. At the center of a black hole, physics breaks down. Singularities are places where the laws of physics break down. Electrons, according to the Standard Model, are "point" particles, but I've never heard of anyone suggesting that singularities lurk inside electrons. Therefore, the laws of physics would seem to apply. So how do you deal with 'point' particles that are not supposed to contain singularities?