Question about extreemly large black holes.

[mrspeedybob]

If we define the density of a black hole to be it's mass divided by the volume within it's event horizon then as the mass of a black hole increases it's density decreases. At some point the density would be equal to the ambient mass density of the universe. Can we correctly consider ourselves to be in such a black hole? Or is there a balance point where gravitation is balanced by cosmological expansion that represents a theoretical upper limit to the size of a black hole?

 

[Simon Bridge]

It's intreguing and has been discussed:
http://www.jimhaldenwang.com/black_hole.htm
(you have to scroll down)

http://www.einstein-online.info/spotlights/changing_places
... much the same thing but with nicer pics.

That would be only the average density of course.

 

[Chronos]

Density is not a useful way of looking at event horizons. The mass density inside the event horizon can be naively approximated this way using the Schwarzschild metric, but, you will get a nonsensical answer. Spacetime geometry is obviously non-euclidean in the presence of extreme mass density. Otherwise, any neutron star in excess of about .25 solar masses should be a black hole. If you apply the Tolman [TOV] limit to account for spacetime curvature it increases to around 3 solar masses.