## Tuesday, April 19, 2011

### Can we see inside black holes?

The last week there was an article that was commented in the arxiv blog: Planets Could Orbit Singularities Inside Black Holes.

The blog entry discuses this article: Is there life inside black holes?.

The article is a pure classical relativity article. It study the possibility of stable orbits for planets inside a black hole, in particular in a Kerr-Newman black hole, that is, a rotting charged black hole. The classical geometry of a Kerr-Newman black hole is described by it's Penrose diagram:

The essential aspect of the K-N black holes for the work of that people is the presence of the inner horizon (a Cauchy horizon). In a non rotating black hole, described by the Schwarschild metric, once he cross the event horizon the radial coordinate changes it sign acquiring a time sign. That means that one must go in the direction of decreasing radius until one finds the central point-like singularity. A common interpretation of that geometry is to say that inside the black hole the space itself is falling toward the centre at the speed of light and it drags averything with it.

In the K-N case things are somewhat richer. In addition to the outer event horizon there is an inner cauchy horizon. When the black holes spins faster and faster (or when the charge of the black hole increases) both horizons get nearest and nearest until, ultimately, they would converge and it would become an extreme black hole.Beyond that one would have a naked singularity but it is thought that such a possibility should be ruled out.

well, as a I said te key point was the cuchy horizon. AS you can read in the linked wikipedia article a Cauchy Horizon is a boundary for the validity of a well posed Cauchy problem in partial differential equations. It can be shown that light (or whatever wave) crossing the horizon gets an infinite blue-shift. That means that it's energy-momentum tensor diverges. The implication of it would be that the back-reaction would destroy the Cauchy horizon once a particle cross it. Still one could get an stable Cauchy horizon if one throws in it exotic matter violating the AWEC (average weak energy condition) well known for people working in wormholes.

The reason why the cauchy horizon is important is because once it is crossed the radial coordinate becomes once again space like. That opens the possibility of the existence of stable orbits inside the black hole. In previous articles, cited by the author, it was shown the existence of that orbits for Reisner-Nordstöm (charged) and Kerr (rotating) black holes. The present article generalizes the results to the general case. In the article considerations are hold about the tidal forces, sizes, radiation rates and they conclude that in a galaxy centre sized black hole a planet could do an stable orbit around the singularity and hold life.

Well, this is the content of the article. As I have explained it is worked in the ansatz of the validity of classical relativity inside a black hole. Also it depends strongly in the stability of the cauchy horizon that can't be got without exotic matter. Note: the author doesn't mention that point about exotic matter although he is aware of the fact that cauchy horizons are not stable. Without exotic matter the whole paper is of a purely academic interest even if one accepts that classical general relativity is accurate to describe black holes inners.

Of course there are a lot of people who don't like classical GR for doing so. In string theory there are many alternative descriptions. On one side one has the correspondence principle of black holes (due to t' hooft and Suskind) that says that an observer falling into a black hole will not be able to notice when he has crossed the even horizon. That means that the physic he sees is must be equal that the physics seen by an outside observer. The reason of the introduction of that principle is the intent of saving unitarity in the presence of Hawking radiation. The actual reasoning is made not classically but for the Hilbert space of a quantum theory as seen but inner and outer observers.

Another string theory inspired viewpoint is described in a classical article by Maldacena: D-brane Approach to Black Hole Quantum Mechanics . In the last part of that article, after calculating the Beckenstein-Hawking entropy, Maldacena Suggest a view where black holes inners and Hawking radiation is described in terms of D-branes. I am not aware if that suggestion has been further developed. I have made a partial search for "hawking radiation in string theory" but I haven't found too much. In fact, beyond that Maldacena article, I found only an approach written some years before using a very aproximative description.

Another paradigm for black hole inners in the string literature would be the fuzzball approach of Mahupart (or maybe Mithur I am not sure at this point and have not time to do a search just now).

Well, that variety of viewpoints, not very compatible among them, for the black hole inner is disappointing. Even in the simpler case of the general relativity viewpoint is disappointing the possibility of the existence of stable structures (maybe planets of an advanced alien civilization, maybe a much more prosaic rings of dust) existing inside the black hole hidden for us from the event horizon.

But, wait! The title of the post wonders about the possibility of seeing inside the black hole. Of course classically it is impossible because of the very meaning of "event horizon". But when quantum mechanics enter the game thing could change. Of course the key would be Hawking radiation. The semiclassical theory says that the radiation must be purely thermodynamic so we can't get any info from it. But if unitarity is conserved the Hawking radiation can't be purely thermodynamic and it must have some structure that stores all the structure of the matter that formed the black hole and that has fallen inside it after it's formation. Possibly it will also have some information about the inner structure of the black hole. Obviously to get that info is very difficult in practice. The usual analogy is to say that one could reconstruct, in principle, the form of a living object from the ashes that are produced when it is burn.

But if we are a little least ambitious maybe we could actually get some partial information. Maybe we could design some easy mental experiment in which throwing into the black hole some specific kind of matter in some specific way we could analyse the Hawking radiation related to it to get some information of the inside of the horizon. That would actually be very cool because it would give an experimental way to distinguish the competing descriptions of the black hole inner.

Of course I actually don't know the details of how this could be done (only a very vague ideas that probably will not work). But maybe something on this purpose is already made and a kind reader would give me the references ;).