# Geometry of a black hole

by Jd0g33
Tags: black, geometry, hole
 P: 293 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?
 Sci Advisor P: 6,038 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.
Thanks
P: 3,458
 Quote by Jd0g33 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.

P: 293
Geometry of a black hole

 Quote by Nugatory 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
 C. Spirit Sci Advisor Thanks P: 5,427 Kerr black holes have 1D singularities (ring).
P: 119
 Quote by WannabeNewton 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?
P: 366
 Quote by Jd0g33 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.
PF Gold
P: 6,107
 Quote by Jd0g33 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.
 Sci Advisor PF Gold P: 9,366 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.
Thanks
P: 3,458
 Quote by Chronos 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?
 Sci Advisor PF Gold P: 9,366 See http://arxiv.org/abs/gr-qc/9803087 for discussion.
P: 2,193
 Quote by Chronos See http://arxiv.org/abs/gr-qc/9803087 for discussion.
??? This paper seems to be discussing only the coordinate singularities at the horizons, not the physical singularities. It's been obvious for a long time that these are mere coordinate singularities, but the physical singularities cannot be removed by any coordinate transform.
 Sci Advisor PF Gold P: 9,366 Agreed. Coordinate transforms do not resolve point singularities as they suffer from infinite curvature, which produces other infinities. Efforts to remove this infinite curvature are being attempted in LQG and AdS/CFT. The Kerr central singularity is rather unique in that there are trajectories that need not pass through a region of infinite curvature. The lure of adding extra dimensions to resolve this singularity, such as in AdS/CFT, is undeniably tempting. Here is a paper some may find of interest: 'Infinities as a measure of our ignorance', http://arxiv.org/abs/1305.2358.

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