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A problem in quantum theory of black holes accessible to a newcomer.

+ 7 like - 0 dislike
673 views

Hi dear physicsoverflow community.

Being a PhD student I'm thinking about changing an area of research. Currently I become interested in the physics of black holes, especially at the quantum level (within the framework of string theory/QFT). My knowledge and understanding is however very superficial at the moment.

The problem is that such questions are somewhat out of the mainstream in my current laboratory but properly posed, they could draw an attention. My feeling is that coming to my advisor and telling him that "I want to work on black holes" without any particular idea for what I'm going to do would be no good.

For this reason I decided to give it a try and ask the community where should I look. I want to find some straightforward but still meaningful scientific problem to work on as I try to enter the new field. Maybe it is possible/reasonable to perform some generalization of the black hole entropy calculation for some particular case or smth. like that. You could suggest the problem itself or give me a more precise idea for where can I look for it.

Aside from the open problems I would be grateful to receive references on some useful introduction/review articles on the subject. I'm currently reading Ted Jacobson's "Introductory lectures on black hole thermodynamics" but found no instances of the pedagogical treatment of the black hole statistical physics, specifically within the framework of the string theory.

Finally, for some reason I don't feel too comfortable with revealing my personal information (name, affiliation etc) in public. Although having a social side to it, I hope that my question is more of the scientific nature and can be answered that way.

Any help is greatly appreciated, thank you.

asked Sep 27, 2014 in Theoretical Physics by Weather Report (210 points) [ revision history ]
edited Sep 28, 2014 by suresh

There is some interesting work relating hydrodynamics to gravity or turbulent diffusion coefficients to blackhole physics, see for example this thread: http://www.physicsoverflow.org/7528/

One simple starting point would be to start with Bekenstein's papers and understand the reasoning that led him to associate an entropy with the area of a black hole.

The next step is to work through Hawking's calculation (Particle Emission by Black Holes) of the emissivity of a black hole. Its a fairly straightforward calculation - solving the equation for a scalar field in a Schwarzschild background. This calculation suggests fairly obvious generalizations - instead of a scalar field, work with a spinor field or a scalar field with internal degrees of freedom, and see if the calculation can be carried out for these and if that gives the same result as for a plain-jane scalar field.

I would not advise you to worry about the stringy or loopy approach while getting started.

If you can cover this ground, then you'll be better equipped to decide which directions to pursue further. Hope this helps :D

4 Answers

+ 6 like - 1 dislike

One of the major achievements of string theory is a detailed accounting for Bekenstein-Hawking entropy by stringy microstates. This is a beautiful subject full of computational detail and actual insights. Some references are collected on the nLab at string theory and black holes. In particular I recommend looking at Sen's 07 lecture notes:

  • Ashoke SenBlack Hole Entropy Function, Attractors and Precision Counting of Microstates, extensive lecture notes (arXiv:0708.1270)

answered Sep 29, 2014 by Urs Schreiber (5,785 points) [ no revision ]

Thank you! Indeed, the links are very useful.

Dear Urs, while nlab is a fantastic repository of knowledge and Ashoke Sen's work is always a great source of inspiration and ideas, I would hardly think Sen's lecture notes are the best place to go for someone trying to find problems "accessible to a newcomer".

But he says he is interested in black hole physics within the framework of string theory/QFT, he said he liked the links.  Also, the hint to Sen's lecture notes Urs has given may be userful for others too...

A newcomer ambitious to wonder about quantum theory of black holes is a different kind of newcomer than one trying to prepare for a science fair. If Sen's lectures don't seem suitable, then one might need to think about choosing a topic less ambitious than quantum theory of black holes in the first place. There is a limit to how much a topic may be simplified. Luckily there are some ambitious students who feel motivated by getting their hands on some of the real stuff.

Yes, and PO answers can not be too high-level by definition ;-), as there are hopefully always some people around who like and appreciate real cool stuff ...

+ 5 like - 0 dislike

A genuine problem I think about sometimes is reconciling the 5d Gregory Laflamme process with the classical no-splitting theorem for black holes (I believe this was brought up in this context by Giddings). The situation is that a line-extended 5d black hole is unstable to splitting into spherical holes, but these can't properly separate in the classical theory, they are linked by tendrils of horizon cylinders that get narrow and presumably connect the black holes to each other classically indefinitely. Gubser analyzed this situation a decade or so ago, looking for a stable end-point, but it seems obvious that there is no stable endpoint, that the black holes must separate completely on physical grounds, theorem or no theorem.

To understand what is going wrong with the classical theorem (it is correctly proved), there is an an analogous paradox in continuum mechanics for viscous fluids (I see it in my electronic cigarette every day!). If you take a viscous fluid, and try to separate a blob into two separate drops, you just can't do it in continuum-mechanics, and for real viscous fluids (like e-juice) you end up having a thin tendril filament linking the two drops forever, and it just becomes more and more tenuous. But the atomic structure of the matter leads the tendril to eventually statistically break, separating the drops.

I strongly suspect that similarly, the ultimately quantum properties of the black hole is breaking the black holes of the end stage of the Gregory Laflamme instability into separate holes. There might be a semi-stable tendril for a long time, as in the viscous fluid drop-separation case, or the tendrils might classically want to become infinitesimal right from the start. It requires study to know.

There are few possibilities for exact solutions to help here (although it is possible to study something similar using exact solutions). But numerical methods are perfect for this problem, as there is cylindrical symmetry and translational symmetry which reduces the computational load to managable levels. You can put it in a box, and do expansions for the solution. So as a numerical GR question, I think it is ideal. A problem regarding this is that the thin tendrils require a nonuniform method of describing the solution, like a nonuniform lattice, as is usual in numerical GR, where the regions of high field are fast-varying and the regions of low field are slow varying. There are wavelet methods that might work here, I haven't studied it in detail, it's just something on the to-do list. It is very accessible problem, and it probably requires quantum black holes to fully understand the process, much as the analogous fluid problem requires atomism for the tearing process of the fluid tendril.

answered Oct 3, 2014 by Ron Maimon (7,535 points) [ revision history ]

These examples of black holes or two blobs of viscous fluids not being completely separable classically reminds me (probably superficially) about black holes being connected by ER bridges ...

So could these problems potentially be attacked by taking some kind of "classical limit" of the ER/EPR business ...?

I thought of it too, I am not sure if there is a meaningful connection either. It's an issue regarding black holes separating that they can't classically separate. The classical version you can study in an exact solution is a small black hole coming out of an eternal Schwartschild black hole from the white hole region. This is a (good) model of a string emission of Hawking radiated black hole, and there is a tendril in this case also, although here the quantum breaking is clearly fast, and I am not sure if it is analogous to Gregory Laflamme. The new Susskind entanglement thing is also difficult to internalize, I am not sure about it being even correct, as the nontraversible condition is strange.

+ 2 like - 0 dislike
answered Sep 28, 2014 by suresh (1,535 points) [ no revision ]
+ 3 like - 1 dislike
answered Sep 29, 2014 by Ryan Thorngren (1,605 points) [ no revision ]

@Ryan Thorngren my impression was that it requires a lot of understanding to work on this question (or to pick a 'correct' unswer from the already suggested). My intention was to find a more straightforward 'calculus' problem to start with.

Nobody knows what will resolve this paradox. It will likely take a leap of physical intuition and only a little bit of "calculus". That's why I consider it elementary. Here's another very interesting and very different approach to the problem http://arxiv.org/abs/1301.4504 .

Lumo thinks there is no paradox at all and that the firewall issue is just a confusion of some people: http://motls.blogspot.com/search?q=firewall ...

Some of his argumants look rather reasonable to me ...

My only response to that is to keep reading. :)

Yep, that is what I do too :-)

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