How can black holes have no volume and infinte density yet have a finite mass?
In: Physics
What’s tripping you up here is that physicists don’t use the word “infinite” in *quite* the same way that mathematicians do. You could say that what black holes have is *undefined* density, because density is (mass / volume) and the volume is zero. And, of course, you can’t divide by zero. So regardless of what the mass is, the black hole’s density is undefined (or infinite, or unbounded).
The slightly more honest answer is that we don’t actually understand what that means in practical terms. It’s probably not *actually* a finite amount of mass with literally zero volume but that’s the best we can figure out with what we can currently observe. Black holes are weird, and the more we learn about them the weirder they get.
Einstein discovered that space itself is bent by the presence of mass within it. You’ve certainly seen the graphic of a bowling ball dropped on a tarp and then a golf ball representing orbit or whatever (if not look it up). A black hole occurs when space is bent so much that it folds in on itself and there are no paths that don’t lead to the singularity and everything, in a run-away reaction of sorts, squeezes down into an infinitesimally small volume.
It’s probably never going to be something you can really visualize or intuitively understand because it is very alien to the human experience. Essentially though it still acts like a mass in space, but it’s weird because space all around it is severely bent, and then if you get too close you realize there is no path through space that doesn’t lead to it’s (so tiny it’s radius is zero) singularity.
A black hole has an infinitesimally small volume, which means that its density (mass/volume) becomes massive, almost infinite. That doesn’t mean that the mass is infinite.
If a black hold had “infinite” mass, it would pull everything into it. The Newton’s law of gravitation states that the gravitational force is proportional to the masses of each body; if one mass was “infinite,” then the other body would be experiencing “infinite” attraction.
Black Holes have a volume, in some senses. The Schwarzschild Radius defines a volume. Inside this volume, we are pretty sure that normal physical ideas like density are not knowable. It’s clearly not solid, but since light can’t get out the space is so curved we only have theoretical explanations.
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