## Monday, October 24, 2005

### Samir Mathur's black holes

If you hear silly songs, it is because of the videoclip included in the previous text.

Today, you won't find a single gr-qc article with at least one sentence that makes sense. Guaranteed.

One hep-th article that could have appeared on gr-qc is by our friends Ghosh, Shankarayanarayanarayanarayan, and Das (sorry, I could not resist!) who confirm using the monodromy method that ln(3) is really, really not a universal feature of the quasinormal modes of generic black holes. Update: their particular paper was wrong because of using wrong topology of Stokes' lines but keep on believing the conclusion that ln(3) is not universal.

There has not been a single article on this blog about Samir Mathur's picture of the black holes. Because I find it exciting - and with probability of order 10% even correct - Samir deserves a couple of words. He has a new gospel

in which he discusses his unconventional ideas about the black hole interior. Note that according to conventional general relativity, the horizon itself can't be identified by local measurements. The black hole interior has an interesting causal structure, and whoever falls into a black hole, can never escape (until the black hole evaporates completely).

George Chapline would argue that we should not trust general relativity and its laws may completely break down at the horizon and its interior can therefore look very different from the conventional picture of general relativity. Well, George Chapline would prefer to replace GR by gossamer superconductors.

Although such a hypothesis about a drastic change near the horizon is only possible when locality is heavily violated, Samir Mathur would probably agree with it. Samir Mathur and Oleg Lunin constructed solutions with infinitely many parameters that can be identified with the microstates of a five-dimensional black hole with two charges. Their interior is "fluffy" and Samir wants to argue that it is a general feature of black holes.

Samir and Oleg start with a general vector-valued function "V^i(t)" that describes transverse fluctuations of a long wound string, and apply a sequence of dualities to construct a non-singular, asymmetric solution of supergravity. If you look closely at this solution corresponding to "V^i(t)", you find out that all singularities are just coordinate singularities and the local geometry is therefore smooth everywhere. Moreover, the solutions have no horizons. The infinite-dimensional space of possible functions "V^i(t)" must be quantized and it leads to the appropriate number of microstates that can be credited for the black hole entropy.

Bound states in quantum gravity such as black holes, Samir argues, may become very large, fluffy objects. They may be as extended as the black hole radius itself, and their two-charge wiggly black hole solutions serves as a moral proof of the concept.

Why are the bound states so extended? Obviously, they look like a bound state of very light, relatively weakly coupled states. Recall that the atom is much larger than the nucleus, for example, and it is because the electron is light and relatively weakly coupled. Samir explains that the black hole is really made of many "bits" which may be interpreted as fractional branes or other fractional objects. For non-extremal black holes, you may imagine that the black hole has a lot of fractional objects "XY-antiXY" where XY represents the charges that would otherwise be in a minority inside the black hole. Each of these "XY" fractional branes is extremely light - and has a small enough charge - so that the physical size of "non-locality" describing the interactions of the "fractionated" objects is always comparable to the black hole radius.

I would like to mention that this "fractionation" may be dual, via the gauge-gravity duality, to the decomposition of gauge-invariant singlet states into many colored constituents. The black hole may be thought of as a composite of many "quarks" in the CFT description, and because there are many of them and they are light, the natural size of the bound state is large.

In the CFT language, we are usually unimpressed by such a large size of the glueball because we believe that the locality in the bulk has very little to do with features that are easy to see on the CFT size. However, Samir wants us to believe that the bound state called a "black hole" has a comparable level of non-locality to its radius.

I actually believe that he may be right in some sense, but the effective physics for most probes will be as local as GR leads us to believe. How can we have physics that is simultaneously almost local as well as very nonlocal? Recall that in Matrix theory, the required bound state of N D0-branes has a radius that scales like N^{1/3} in eleven-dimensional Planck units. It becomes infinite as N goes to infinity; nevertheless, it should describe a graviton in 11 dimensions which is essentially a point-like object.

Something similar must be happening in Samir's picture if it is correct. His picture of the black hole looks extremely non-local but when you try to calculate some typical process, you will find out that physics may be described, with a rather good accuracy, as local physics that follows from general relativity, including the horizon. However, the non-locality as envisioned by Samir may still be used to guarantee that the information may slowly escape from the black hole interior and be encoded in the outgoing Hawking radiation.

It is rather hard to prove this picture although it may very well be correct. The truth is that we have not really understood, in some intuitive way, why the huge fluffy bound states of D0-branes in Matrix theory behave so incredibly locally. I also believe that we should first understand how the large bound state of N D0-branes may be approximately described as a bound state of smaller number of bound states, each of them being "approximately" gauge-invariant under a smaller gauge group. Also, we should understand the scaling of "N" as a kind of generalized renormalization group flow.

Even though the local physics involving the bound states of D0-branes essentially follows from dualities and M-theory, the best picture how to explain this apparent "miracle" is to argue that most of the D0-branes' wavefunction that is spread to large distances actually arise from some very high-frequency degrees of freedom whose effect is averaged out if you probe the system with any reasonable, finite energy probe. (It would be nice to know how to "integrate them out" and use approximate degrees of freedom in which the bound state looks small.) The same comment applies to strings in perturbative expansion themselves: their squared average size is also logarithmically divergent, but this divergence is regulated if we impose a UV cutoff on the worldsheet - something that is interpreted, in this particular case, as a UV cutoff in spacetime.

Someone should try to describe the functioning of these ideas in a slightly more coherent and quantitative fashion. Such a complete answer should illuminate the following questions:

• are gauge-non-invariant states good degrees of freedom to describe the black hole interior in the dual CFT description?
• what kinds of objects are able to probe this fine structure? What are the length scales of non-locality measured by various probes?
• is there an explicit link between Samir's fractional branes and the gauge-non-invariant ingredients of the black hole?
• can you evaluate the total amount of information per unit time that the non-local part of dynamics is able to emit from the black hole?
• do you solve the information paradox by a careful compromise and interrelations between the black hole's local and non-local dynamical processes?