A black hole has no hair, but can it have cellulite?

Question

A well known conjecture of general relativity is that a "black hole has no hair", i.e. once matter has disappeared behind the event horizon, the information about what detailed properties this matter had (except mass, (angular)momentum and charge), before it went into the hole, is thought to be lost.

But I was asking myself if a black hole does, from the outset, have a spherical event horizon and an essential singularity in the center, or if the event horizon can experience dynamic surface waves ("cellulite" to put it pointedly) and if the interior solution could have no singularity at all (because the matter that collapsed inside the horizon is still falling to the center). In this picture, I would expect the spherically symmetric solution to be the equilibrium state of the black hole when all surface waves have been dissipated to the surroundings and all matter inside of it has fallen to the center.

Is this picture incorrect?

Answer 1

Due to gravitational time dilation, a distant observer never actually sees anything reach or cross the event horizon of a black hole. Instead, infalling objects are increasingly red-shifted as they approach the event horizon until they disappear for all practical purposes. Therefore an external observer has no way of telling whether infalling objects have reached the singularity at the centre of the black hole (if, indeed, there even is a singularity). The “interior” of the black hole is completely casually disconnected from its exterior - in one sense, for a distant observer, the black hole had no interior at all.

The closest thing I can think of to “surface waves” on a black hole is the process of “ringdown” when two black holes merge. The event horizon of the merged black hole undergoes a short period of rapid oscillation before it settles into a stable configuration. This process of ringdown generates gravitational waves, which have been observed.