# What is the shape of a black hole?

I was thinking; what shape does a black hole have?. By 'Shape', I mean its form (e.g, circle , cylinder, sphere, torus, etc..).

We usually think of black holes as if they're plugholes (e.g, a flat circular object), but what if they're spherical? A spherical black hole would make much more sense. I would imagine than a black hole shaped like a basketball would be capable of pulling more mass towards it than a flat one, as it has a higher surface-to-volume ratio to do so.

Edit I know that it's probably a sphere, but when you think about it, a cylinder could also be a potential shape.

• anything such large gravitational force cannot acquire any other shape than a sphere Jul 31, 2013 at 14:58
• @Akash: As described in John Rennie's answer, a rotating black hole is a counterexample to your claim.
– user4552
Nov 13, 2014 at 16:53

A stationary uncharged black hole is described the the Schwarzschild metric:

$$ds^2 = -\left(1-\frac{2GM}{c^2r}\right)dt^2 + \frac{dr^2}{\left(1-\frac{2GM}{c^2r}\right)} + r^2 (d\theta^2 + sin^2\theta d\phi^2)$$

The event horizon is at $r = 2GM/c^2$, where the $dr^2$ term goes to infinity, so it is a surface of constant $r$ i.e. it is indeed a sphere.

Your plug hole analogy comes from seeing 2D representations of the black hole geometry in text books. This is only intentded as an analogy and is somewhat misleading. The metric tells you what the geometry actually looks like.

A stationary but charged black hole actually has two event horizons, and both are spherical. The rotating black hole also has two event horizons. The outer is an oblate spheroid: I'd have to go away and look up the shape of the inner.

I don't know of any system that would have an event horizon shaped like a cylinder, though I wouldn't rule out the possibility that a suitable shaped system might have an event horizon shaped like an infinitely long cylinder i.e. with no ends.

• Presumably Tippler's metric might be fiddled with to get a cylindrical event horizon - I don't have access to his thesis but my curiousity is piqued ... Now I've just read the Black String answer, so I'll really have to find out what precludes a cylindrical event horizon now! Aug 1, 2013 at 3:42

To add to John's answer: black hole with nonzero angular momentum is represented by Kerr metric. It's horizon is a spherical surface, but it also has a special surface: ergosphere that is oblate spheroid touching horizon at two 'poles'. The no-hair theorem of black hole physics precludes them from having more complicated shapes, because such shape would have generated noticeable 'hairs' that the outside observers could feel.

The cylindrical black hole would be so-called black string solution. This do not exist in the ordinary general relativity, however they appear as solutions in the higher dimensional generalizations of GR (where space-time dimension D>4). These have horizons 'shape' of manifold $\mathrm{R}\times S_k$ (or $S_1 \times S_k$ if the dimension along the string is compactified, $S_k$ is a k-sphere).

Also such higher dimensional generalizations of general relativity have black branes solutions which have horizon geometries of $R^p \times S_k$.

Another type of 'odd' black hole geometry occur within context of brane world. If our world is represented by a membrane in some higher dimensional space then what would be the higher-dimensional geometry of black holes in our world? The answer could be black string mentioned above (intersecting our world) or something like the black pancake embedded in our brane.

• It'd be nice to mention that BH no-hair theorem applies only to equilibrium (stationary?) solutions. Surely when two BH are merging they have a different shape. Dec 14, 2018 at 8:49

The event horizon of a non-rotating black hole is spherical. The "pit" illustration represents the gravitational well created by the hole. It demonstrates the "warping" of spacetime described by the equations of general relativity.