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

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?

• Related: physics.stackexchange.com/q/937/123208 I quite like this line from Stan Liou's answer: "rather than gravity having a special property that enables it to cross the horizon, in a certain sense gravity can't cross the horizon, and it is that very property that forces gravity outside of it to remain the same". Commented Feb 2, 2021 at 16:45
• @PM2Ring: but that property does not enforce a strictly spherically symmetric gravitational field outside the hole. The black hole exterior is subject to boundary conditions, just like any other gravitational field. So my question basically boils down to: can the event horizon strictly be homogeneous as a spherical boundary condition when the volume in its direct vicinity is filled with arbitrarily complex fields. Or, put as an electromagnetic analogy: the electric fields outside a spherical conductor determine the charge distribution on its surface and vice versa. If and why not for gravity? Commented Feb 2, 2021 at 17:07
• " that property does not enforce a strictly spherically symmetric gravitational field" That's true, but there's bound to be at least a high degree of circular symmetry, due to the angular momentum. Commented Feb 2, 2021 at 17:37