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.
In: 1
Note first that you exactly know the mass of any object just by how they bend spacetime. Also note that a “singularity” is not just the exact point where things go bonkers, but includes the behaviour around it; a singularity cannot exist on its own without the “non-singular” space around it. (Math talk: Formally, one would talk about the system of neighbourhoods of a point to formalize this in _stalk_-like manner.)
It is better to not think about black holes as points of infinite density of a fixed mass when trying to properly work with them. Instead, consider it as the spiky (i.e. singular) bump in spacetime itself. The mass-energy that caused it is represented and preserved in the bending it caused.
> Also, are all singularities the same and behave the same and have the same properties, regardless of the mass of the black hole?
Similar to elementary particles, black holes are determined by a small list of properties: mass, charge(s), and spin. In reality, black holes should usually be effectively uncharged, but of quite relevant mass and with spin. The same still holds true for the singularity itself, as long as you understand it as outlined in the first paragraph.
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