# Bumpiness in event horizon due to infalling matter

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Classically, far-observers never see infalling matter to traverse the event horizon, they only see bumps that are progressively red-shifted. My question is: how quickly these bumps even out across the event horizon surface?

For instance, can I make a bump to grow faster than it spreads out in a steady manner? Can I make cusps in the event horizon via such methods?

If joining multiple of such bumps is physically possible, you could create an event horizon with a handle, which would be topologically equivalent to a toroidal black hole

asked Jun 16, 2014
edited Jun 16, 2014

## 1 Answer

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These are called the black-hole normal mode decay rates, the decay is analogous to a membrane with a certain viscosity type friction which is dissipating it's energy, and the rate of exponential smoothing out of surface fluctuations is the rate at which the black hole equilibrates. The identity of the two processes, the membrane-paradigm surface smoothing from dissipative dynamics and the string-theoretic equilibration of the dual field theory, was a major motivator for the holographic principle in the 1990s. The normal mode rates are calculated in several places, I don't remember the rates offhand.

Regarding "making cusps", a steady insertion of matter flowing in a line-stream into a black hole should make something like this, but I never saw the precise form of the metric, or the deformation of the horizon, but it should make a cuspy structure of some kind. There are other singular constructions which are easier, involving time-reversal of black hole merger, but I don't remember how they work. Another cusp is the path of transition between a 5d linear black hole and a line of 5d sphere black holes, the Gregory Laflamme instability. The 5d black hole has to break up, but the way it does so is by producing many black holes linked by thin horizon tubes, which are singular cusps at the point where they connect with the large horizons. The scaling limit of this is computable, but it has never been done in the literature.

answered Jun 16, 2014 by (7,580 points)
edited Jun 16, 2014

Nice answer :-)! Is the link between the black holes in the line similar or related to the link between black holes by entanglement in the context of the ER/EPR correspondance?

Hi Ron. So, if doing cusps is physically allowed, then joining several cusps would also be possible, which would result in a toroidal event horizon (actually just an event horizon with a handle, but topologically equivalent)

In 5d, toroidal horizons exist, and exact solutions are known. The transition between these and spherical horizons are known. The problem with the cuspy type things is that they are unstable, and in 4d, when you try to link them into a loop they collapse too fast to do so. There is no problem in 5d, though.

@dilaton: I don't know, I don't understand ER/EPR well yet.

The problem with the cuspy type things is that they are unstable, and in 4d, when you try to link them into a loop they collapse too fast to do so

but wait a minute.. Once I'm growing the bump (feeding it at least an order of magnitude faster than it can spread out, I can assume that I'm firing mass at the bump relativistically if you like) why would it matter in what direction the bump is grown? The question is if it can be done fast enough so that some null rays can make it through the handle before it evens out.. Probably there is where the construction fails to achieve a true toroidal horizon, even transiently

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