general relativity - 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.

Answer

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.