# Is there a limit to the size of black hole?

I have read answer by @John Rennie in regards to the size and density of black hole. In the last sentence he states that super supermassive black hole with the mass of 4.3 billion Suns would have a density equal to one i.e. the same density as water.

Does that mean that there is a limit to the size of black hole? (otherwise I should be able to swim in it). What am I missing here?

## 1 Answer

As stated in the answer you linked, the density of a black hole is defined by the ratio of its mass over the volume spanned by its Schwarzschild radius. That does not mean that there is actually uniformly distributed matter inside the Schwarzschild radius. All of the matter is packed very densely (in something with the characteristic length of the Planck scale) around the singularity ("classically" i.e. without quantum gravity, the density is zero everywhere but in the center, where it is infinite. This is why it is defined in the other way). You certainly can not swim in a supermassive black hole.

• Hi Noldig, thanks for your answer. So if matter (or whatever it is when forces merge) is more densely packed closer to the singularity that would imply that it should be less dense the further away one would go from it, then wouldn't it mean that density at the edges of black hole would be even less than that of water? – Matas Vaitkevicius Feb 9 '16 at 14:39
• the "density" as you think of it is zero everywhere besides in the singularity where it is infinite (all the mass of the BH in a point). By very densely I mean in the volume of something with the characteristic length of a planck length. – Noldig Feb 9 '16 at 14:42
• I see, density drops because the bigger radius event horizon is - the more space has to be added when calculating average density, very clever! Thanks Noldig. – Matas Vaitkevicius Feb 9 '16 at 14:43
• Thats the point. You're welcome – Noldig Feb 9 '16 at 14:44
• I don't think the density is zero everywhere. The Schwarzschild black hole is formed by spherically infalling matter. From the outside you can only see the total mass, but the matter inside never really reaches the singularity. EDIT: Or is the inside solution defined as timetranslational invariant? Then of course the only possiblity would be to have all matter in the singluarity in the center. – dan-ros Feb 9 '16 at 14:56