Astrophysics Question (Black hole)

The black hole at the centre of IC 1101 has a mass of 7.1 × 10^11MS where MS is the mass of the Sun.
Calculate the average density within the event horizon of the black hole.

I'm using the P = m/v formula, then rearranging that to contain the volume of a sphere (for the actual black hole), and then the Schwarzschild radius to get the event horizon, this gives me the equation: https://i.imgur.com/ZUOHWml.png

and when subbing in the numbers given
Ms = 1.99*10^30kg
m = 1.4129*10^42kg
G = 6.67*10^-11m^3 kg^-1 s^-2
c = 3.00*10^8ms^-1

I get the answer of the density being equal to a number to the power of -5, which when searching up the average density of a black hole to check against reality seems much to small to be correct, anyone able to help if I messed up with the equations or numbers used?

Reply 1

lordaxil

No, you're absolutely correct - in fact the answer is more like 10^-8in standard units for density of g/cc.

The point of the question is to show that "density" of supermassive black holes is in principle very low if you define their "size" as being related to Schwarzschild radius. Of course, in reality, all of the mass would be concentrated near the singularity at the centre of the black hole so defining their density in this way is not very meaningful.

Reply 2

Arecedia

ahh, thanks then, I just searched up the density originally and it was around 10^19, although after reading over it more carefully that was for a black hole with a similar mass to the sun, thanks for replying though