gravity - Is a black hole a perfect sphere?

As I understand it, general relativity says that there's gravitation everywhere in the universe, and this gravitation creates dips in space, so to speak, often represented in 2D as a weight on a rubber sheet, like the picture below.

Source,

so, a black hole might generate a perfectly spherical event horizon, but it generates it on a not perfectly flat 3 dimensional surface, and I think the gravitation from other objects makes it not quite a perfect sphere. For example, a star or planet that orbits a black hole would drag around a ripple on the event horizon as it orbits the black hole.

Precisely what shape that ripple would be . . . I'm not sure. That said, if you had a black hole as the only object in a universe, then I think the event horizon might be a perfect sphere, or as perfect as possible, given quantum fluctuation, hawking radiation and the impossibility of precise observation and all that good stuff.

Non black holes tend to have lumpy/inconsistent gravity - see here. Even Neutron stars have some inconsistency, but Black holes probably avoid that because the matter is condensed to a point, so there's equal gravitational pull from all directions from the singularity.

Now a Kerr black hole, that's a whole different question. I'm not smart enough to try to answer that one. That might not be a sphere at all.