Can a black hole really have zero volume?

Nothing can have zero volume according to Quantum Mechanics. In QM no object can be confined to a region smaller than its wavelength. Point masses are convenient in Newtonian gravity calculations, but have no reality. read more

The black hole certianly has a volume when viewed from outside. We can take a “snapshot” and measure it. Inside a black hole, when time is constant, r always equals the Schwarzchild radius. In other words, when time doesn't move, the radial coordinate can only have a single value. So the radial distance is 0 when we make time distance 0. read more

Once you have put all these things together, you can calculate the volume of a black hole, as the integral of a certain quantity associated with the metric tensor (the square root of the determinant of its spatial projection) over the spatial"part" of your spacetime. read more

well, black holes dont have zero volume. google the schwarzchild radius. The schwarchilds radius isn't the black hole itself though, its a length proportional to the mass of the black whole which expresses how far light can't escape. read more

Its perfectly reasonable for a black hole to be described as a singularity because when you attempt to solve the equations for its mass and gravity you end up with an undefined region. That the behaviour of space/mass at the centre of a black hole is undefined tells us that there is something missing in our understanding of gravity, relativity and quantum theory. read more

A black hole can be any size. At least up to some as-yet unknown upper limit. The smaller a black hole is. The more dense. The largest super massive black holes are less dense than water. Of course how we measure the size of a black hole is based on the size of it's event horizon which is the point where no information that enters it can exit. read more