Black holes and General Relativity

[Snaar]

Hello everybody, I was watching a documentary about black holes the other day and I noticed something odd.

General Relativity is said to break down when you apply the mathematics on a singularity. In this case, the center of the black hole. The radius of a singularity would be 0. Now there was my problem. I was learned that the smallest possible length, is Planck's length (1.616199 × 10-35) meters. I guess that the radius of a singularity would have to be the shortest possible length.

What is your opinion on this? And where did I (probably) make my mistake in my 'logic'?

Thanks in advance!

 

[PeterDonis]

I was learned that the smallest possible length, is Planck's length (1.616199 × 10-35) meters. I guess that the radius of a singularity would have to be the shortest possible length.

The concept of a shortest possible length comes from quantum gravity; in classical General Relativity, there is no such thing. That's why the standard classical GR theory of black holes has a singularity at r = 0.

However, it is true that the presence of the singularity at r = 0 in the classical theory is one thing that indicates, to many physicists, that the classical GR theory breaks down at this point; and the best current guess we have right now as to the point at which it breaks down is at a length scale on the order of the Planck length. That doesn't mean that the radius of the singularity is the Planck length instead of zero; it means that, when we have discovered the right theory of quantum gravity, we expect that there will no longer be a singularity at all; instead some new physics will come into play at length scales on the order of the Planck length.

We don't have a good theory of quantum gravity yet, so all this is really speculation (educated speculation, but still speculation) until we do.

 

[Snaar]

Alright, I get what you mean. I'm going to search some quantum gravity theories, I don't really get the concept of that.

Thanks for answering!