system
Given the following post, respond as if you're commenting on Reddit:
human
What is denser: A black hole or a neutrons star?

Thank you.
gpt
**Short answer:** It depends what you mean by the 'density of the black hole.'

**Long answer:** Neutron stars are generally taken to be the densest form of matter, since black holes are more of a feature of spacetime than a kind of matter with any typical thermodynamic descriptors (pressure, density, etc).

The cores of neutron stars reach densities a few times greater than that of atomic nuclei at their cores, maybe reaching around 10^15 grams/cm^(3). For comparison, that's like squeezing Mt Everest into a cup of coffee. 

Black holes, meanwhile, have reached the point where no interparticle forces can resist further compression, and so all the matter that was used to make them gets scrunched together at a single point called the singularity. Effectively, this acts like it has 'infinite density' since all the mass of the black hole accumulates here and it is pointlike with zero volume. In this sense, black holes are always denser than any matter outside of one.

On the other hand, a black hole does have an 'average density' which can be defined from the size of its Schwarzschild radius, which is like the distance from the singularity to the event horizon (the point of no return where the escape velocity is greater than the speed of light). Black holes have this funny property where *larger* black holes have *lower* average densities. This is because the radius grows linearly with the mass while the volume grows like the radius cubed, so the 'average density' decreases like the radius squared - double the mass and radius of a black hole and you've reduced it's average density by a factor of four. In this sense, any black hole more massive than about 3 solar masses is *less dense* than any neutron star!