formulaically, i understand the math. My question is more on the theoretical behaviour of something like a singularity.
How can something have zero volume but infinite density? How can something that don’t exist be infinitely dense?
Also, are all singularities the same and behave the same and have the same properties, regardless of the mass of the black hole?
For eg. A blackhole with 100 million solar mass vs another with 10 million solar mass. You take both mass, divide them by zero, and you get the same answer- infinite density.
Sorry for the juvenile question, maybe i shoulda posted this in nostupidquestions instead.
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The word “singularity” comes from mathematics. It’s a place where a function’s behavior breaks down, and it stops behaving according to the rules that govern well-behaved functions.
If you ignore the effects of quantum mechanics, a black hole has zero size. Since mass is conserved, it must somehow collapse its initial mass into that zero size, and (finite mass) / (zero volume) = (infinity density). (More formally, you can think of the density as being the mass times the [Dirac delta function](https://en.wikipedia.org/wiki/Dirac_delta_function), which is how you get different infinite densities in some sense.) But it is not generally believed that this is actually the way the physics of real physical black holes works.
We don’t understand how quantum mechanics and gravity work together. (General) relativity and quantum mechanics make different predictions at extremely high energies and extremely small length scales, and of course the center of a black hole involves both. An understanding of what actually happens at the singularity depends on understanding how gravity works in a quantum-mechanical sense, and that is an active current area of research in physics with almost no known answers.
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