One of the most massive Supermassive Black Hole observed is the one at the centre of the galaxy NGC1600 with a mass of 17 billion suns. It would have a density of ∼0.01kg/m^3, or one part in 100,000 times the density of water, or 1% the density of earth atmosphere at sea level.

But if there is so much gas why isn't the bh shrinking and becoming more dense as gravity would pull everything together?

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    $\begingroup$ What is your source for the density? $\endgroup$ – Sir Cumference Jun 25 '16 at 11:40
  • $\begingroup$ Hossam Aly Astrophysics Ph.D $\endgroup$ – Marijn Jun 25 '16 at 11:44
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    $\begingroup$ The density of a BH isn't really defined, or would be infinite since it's a point. A BH has already shrunk as much as it possibly can. If you wish you can calculate its mass divided by the volume inside its Schwarzschild radius. For M = 17e6, this gives 64 g/cm³. $\endgroup$ – pela Jun 25 '16 at 12:06
  • $\begingroup$ radius = 2MG/c^2 hyperphysics.phy-astr.gsu.edu/hbase/astro/blkhol.html The big ones get positively ethereal, density-wise, calculating from the Schwarzschild radius. $\endgroup$ – Wayfaring Stranger Jun 25 '16 at 12:58

A black hole is not a solid or gaseous body. It is a shape that space-time can take. Now the event horizon is sometimes treated as being the "edge" of the black hole, but there is nothing at this edge. The black hole can't shrink its event horizon, since the event horizon is not a physical object

There is no matter inside the black hole (for this reason the shape of space-time around a black hole is sometimes called a "vacuum solution" of Einstein's equations). The mass of the black hole is concentrated at the singularity (which, due to the curving of space time you can imagine as more like a point in time that you can't avoid if you cross the event horizon.

Since the radius of the black hole's event horizon is proportional to the mass, the volume of the black hole is proportional to the cube of the mass. If you double the mass, you increase the volume by a factor of 8.

Density is mass/volume so if you double the mass you change the density by 2/8=0.25, so the more massive a black hole is, the lower is the average density of the region inside the event horizon.

This does mean that if you did manage to find a gas cloud with 17 billion times the mass of the sun (much bigger than any known nebula - Orion Nebula M43 is only a few thousand solar masses) and you were to somehow compress it to a sphere with 0.1 atm pressure, it would undergo gravitational collapse and form a black hole.

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