A black hole can be less dense than air
If density means mass divided by the volume inside the event horizon, then a sufficiently massive black hole is less dense than water, and a still larger one is less dense than air.
The Schwarzschild radius grows in proportion to mass. Volume grows as the cube of that radius. Average density therefore falls as one over mass squared. Stellar black holes are enormously dense by this measure. A black hole of a few hundred million solar masses — the size of those in large galaxies — has an average interior density near that of water. Go up another factor of a hundred in mass and the average falls below air.
Nothing about this makes the horizon optional. The average is a bookkeeping device over a volume you cannot survey. The curvature at the horizon of a huge black hole is gentle. You still do not come back out, and the singularity, in the classical theory, is still there.
Caveats
- This is not the density of some material sitting at the horizon. It is mass over the horizon volume.
- Real astrophysical black holes rotate, which changes the interior description. The scaling — bigger means less dense on average — survives.
Sources
- 1Hartle J. B.. Gravity: An Introduction to Einstein's General Relativity. Addison-Wesley, 2003.