# Geometry of a black hole

jaydnul
I was watching a documentary about the universe and it claimed that black holes were sometimes as small as 2 kilometers across. Now before this, my general understanding of a black whole was that it had no physical extent in space, that it was just a 1 dimensional singularity, and the black planet looking thing was just where the point of no return started. So if I were sucked into a black hole, would I eventually run into a very dense mass 1 kilometers across or would it just be empty space all the way down to the singularity?

The 2 km refers to the outside dimension. No one really knows what happens inside a black hole. General Relativity and Quantum thoery don't work together - new theory is needed.

Mentor
I was watching a documentary about the universe and it claimed that black holes were sometimes as small as 2 kilometers across. Now before this, my general understanding of a black hole was that it had no physical extent in space, that it was just a 1 dimensional singularity, and the black planet looking thing was just where the point of no return started. So if I were sucked into a black hole, would I eventually run into a very dense mass 1 kilometers across or would it just be empty space all the way down to the singularity?

When people refer to the size of a black hole, they mean the size of the event horizon, the thing you're calling "the point of no return". Classical general relativity does predict that there is a point-like zero-dimensional singularity inside the event horizon at the center, but
- That's just a part of the black hole, not the whole thing. The whole thing is the event horizon and everything inside it.
- We can't very well look inside the black hole to see what's at its center, but it's unlikely that there's really a pointlike singularity. At very small distance scales we have to pay attention to quantum mechanical effects; general relativity doesn't consider these, so its predictions cannot be completely trusted when very large masses are concentrated into truly infinitesimal volumes on the way to becoming a size-zero singularity.

A smallish correction: You said "1 dimensional" above but I assume you meant "zero-dimensional"; a one-dimensional singularity would be a line not a point.

jaydnul
A smallish correction: You said "1 dimensional" above but I assume you meant "zero-dimensional"; a one-dimensional singularity would be a line not a point.

Ya that's what I meant :). Thanks for the clarification guys

Kerr black holes have 1D singularities (ring).

94JZA80
Kerr black holes have 1D singularities (ring).

so a Kerr BH singularity is not literally a 2D disk, but rather just the 1D curved line that comprises the disk's circumference? since we can't peek inside the EH and look and see the "singularity" directly, do there exist any predictions about the range of diameters of the disk formed by a Kerr 1D singularity? if so, i'm assuming it would depend on the BH mass and spin rate? also, when discussing Kerr BH's, why do we still refer to the "final destination" as a singularity when, if it is truly a 1D ring, it is not composed of a single point, but infinitely many points?

Philosophaie
black holes were sometimes as small as 2 kilometers across.

If you look at the way they are formed. They begin with a massive implosion of very large red giant Stars leaving only a small Black Hole as its remnant.

Gold Member
2021 Award
I was watching a documentary about the universe and it claimed that black holes were sometimes as small as 2 kilometers across.

There is nothing that inherently limits the size of a black hole. They could exist much smaller than 2KM across (the EH diameter), but the smaller they are the quicker they evaporate due to Hawking Radiation so really small ones wouldn't last long.

Gold Member
The singularities in a Kerr black hole are coordinate singularities. They can be resolved by changing the coordinate system. There is a strong belief a similar solution is possible to eliminate the singularity in a Schwarzschild black hole, although it remains to be demonstrated.

Mentor
The singularities in a Kerr black hole are coordinate singularities. They can be resolved by changing the coordinate system

What coordinate transform gets rid of the singularity?