Shape of Black Holes: Clarification Needed

[jlroitman]

I am interested in the theoretical shape(s) of black holes. I read that they may be cone shaped, they made be "shells", they may be two dimensional, etc. Can i get some clarification?
thanks, jlr

 

[Mike Cookson]

Surely if they are a true singularity it doesn't have a shape as it has no real physical dimensions. I would have thought that if anything it would be a sphere, certainly the event horizon is spherical as far as I am aware.

 

[Chronos]

Spherical, in the classical sense, seems reasonable. Think horizon.

 

[xantox]

I am interested in the theoretical shape(s) of black holes.

By "shape of a black hole" we should mean its event horizon topology.

By Hawking's theorem, all stationary black holes in general relativistic 4D flat spacetime must have a 2-sphere topology. However, black holes in higher dimensional spacetimes may be nonspherical, an example is the Emparan-Reall black hole in 5D flat spacetime which is a $$S^1 \times S^2$$ ring.

 

[marcus]

I am interested in the theoretical shape(s) of black holes. I read that they may be cone shaped, they made be "shells", they may be two dimensional, etc. Can i get some clarification?
thanks, jlr

There is no scientific reason to suppose that singularities exist in nature. A singularity is a place where some manmade theory breaks down and gives meaningless results, like infinities. So singularities exist in theoretical models.

Typically improved models eliminate them, and this has been happening in the case of cosmological and black hole singularties. As the model is improved one expects to get rid of the glitches, i.e. the singularities.

So your question is about theoretical shapes, shapes in some not necessarily realistic idealization. Fair enough.

The horizon of a nonrotating black hole is spherical.
The horizon of a rotating black hole is NOT SPHERICAL. It is an oblate ellipsoid (roundish but fat around the middle.)

Typically what what people mean by the "singularity" is the place where classcial vintage 1915 General Relativity blows up. In the nonrotating case this is a point, and in the rotating case I am told it is a RING. If I'm wrong I hope someone will correct me about this. I'm talking ordinary 3+1 dimensions here, no extra dimensions.

In any case one shouldn't worry too much about the singularities look like because they are not considered real. We don't expect nature to exactly conform to 1915 classic GR!

 

[xantox]

The horizon of a rotating black hole is NOT SPHERICAL. It is an oblate ellipsoid (roundish but fat around the middle.)

No, this is the ergosphere. The Kerr black hole event horizon is spherical.

 

[MeJennifer]

In the nonrotating case this is a point, and in the rotating case I am told it is a RING. If I'm wrong I hope someone will correct me about this.

It is none of the above since these type of singularities are not even on the manifold.

You might enjoy the final postings on https://www.physicsforums.com/showthread.php?t=170829

 

[jlroitman]

All very interesting. why, may i ask does the event horizon define this theoretical shape? is the "rest of the black hole" a non-entity? or is it the singularity that is referred to above. i thought that the black hole culminated in the singularity. does all this mean that the black hole consists of (theoretically, of course) an event horizon that may or may not be spherical and a singularity and nothing else in-between?

 

[xantox]

The event horizon is relevant, since the black hole is basically an entity made of space. So, you may look at the geometry of this very particular space in order to talk about a shape.

About the "rest of the black hole", this depends on the theory used to describe it. In the classical theory, the interior details cannot determine the exterior description. In quantum theory, singularities tend to disappear.

Physical black holes cannot be empty "in-between", even in classical general relativity, as if you throw things into them, they will for some time exist "in-between".