PHYSICS W3072y
Welcome to the home page for the Spring '05 course "Current Research Topics" (aka Senior Seminar and/or Physics W3072), taught by Prof. W.A. Zajc. I will use this page to announce homework and other course-related information.
How to reach me: My office hours are by appointment; that's so you can be sure of finding me. There's lots of contact information on my home page, my preferred mode (other than in person) is by e-mail at zajc@nevis.columbia.edu. I am on campus Mondays, Tuesdays and some Fridays.
Lectures: Tuesdays 5:30-6:45 pm, 705 Pupin (the day of the week may shift, especially in February when I am traveling extensively)
Texts :
Description: After a 2-3 introductory lectures by the instructor, each student will take a turn leading a given week's discussion. (You may work with another student if you like, but this increases the chances that you will be asked to do another week, since Nweeks > NStudentPairs .) You should choose a topic on some aspect of "black hole physics", but this can be broadly interpreted (e.g., a discussion of the general relativistic corrections required to make GPS work). I would very much like the topic of black hole entropy to be developed. Other possible examples are time travel(??) via black holes, observation of black holes, energy extraction from black holes, the relationship(?) between black hole physics and strong interaction physics, etc. etc. In each case, you should pick a particular paper or papers to work through, and announce them to the rest of the class so that they can read them before coming to class.
Homework: None, other than preparing for your presentation(s) and reading the papers chosen by others.
Examinations: None
IMPORTANT
REFERENCES
In the age of Google, it seems somewhat superfluous to maintain a big page of links to material. Here a just a few that might be useful to get going:
The first student-led session will be presented by Ben Hooberman on Thursday, February 17th at the usual time (5:30 pm). The general topic will be on black-hole entropy; Ben may circulate something to the class list to provide the appropriate background. The below papers and/or references therein may be useful. Note also the various links above, they too may be useful.
1) STATISTICAL BLACK HOLE THERMODYNAMICS.
By J.D. Bekenstein (Ben Gurion U. of Negev),. 1975.
Published in Phys.Rev.D12:3077-3085,1975 ( Phys. Rev. D Server )
2) THE BEKENSTEIN FORMULA AND STRING THEORY (N-BRANE THEORY).
By Amanda W. Peet (Santa Barbara, KITP),. NSF-ITP-97-148, Dec 1997. 48pp.
Published in Class.Quant.Grav.15:3291-3338,1998
e-Print Archive: hep-th/9712253
- References |, Abstract and Postscript and PDF
The next
student-led session will be presented by Kaitlin Kratter on Tuesday,
March 1st at (more-or-less) the usual time (5:30
pm). The reason for the ambiguity in the start time is that
you are all encouraged to attend the
special lecture by Roger Penrose at 4 pm; if this runs long, class will
start a little late.
The general topic will be "Unruh radiation", that is,
the apparent temperature of the "vacuum" detected by accelerated observers.
The below
papers and/or references therein may be useful.
Simplified derivation of the Hawking-Unruh temperature for an accelerated observer in vacuum
Authors: Paul M. Alsing, Peter W. Milonni
Journal-ref: Am.J.Phys. 72 (2004) 1524-1529A detector undergoing uniform acceleration $a$ in a vacuum field responds just as though it were immersed in thermal radiation of temperature $T=\hbar a/2\pi k c$. A simple, intuitive derivation of this result is given for the case of a scalar field in one spatial dimension. The approach is then extended to treat the case where the field seen by the accelerated observer is a spin-1/2 Dirac field.Full-text: PostScript, PDF, or Other formats
Spacetimes with horizons show a resemblance to thermodynamic systems and it is possible to associate the notions of temperature and entropy with them. Several aspects of this connection are reviewed in a manner appropriate for broad readership. The approach uses two essential principles: (a) the physical theories must be formulated for each observer entirely in terms of variables any given observer can access and (b) consistent formulation of quantum field theory requires analytic continuation to the complex plane. These two principles, when used together in spacetimes with horizons, are powerful enough to provide several results in a unified manner. Since spacetimes with horizons have a generic behaviour under analytic continuation, standard results of quantum field theory in curved spacetimes with horizons can be obtained directly (Sections III to VII). The requirements (a) and (b) also put strong constraints on the action principle describing the gravity and, in fact, one can obtain the Einstein-Hilbert action from the thermodynamic considerations. The latter part of the review (Sections VIII to X) investigates this deeper connection between gravity, spacetime microstructure and thermodynamics of horizons. This approach leads to several interesting results in the semiclassical limit of quantum gravity, which are described.
28-Feb-05: I just learned today of this book: An Introduction To Black Holes, Information And The String Theory Revolution: The Holographic Universe, by LEONARD SUSSKIND, James Lindesay, which pretty much seems to be the topic of this course.
17-Mar-05: The entire question of black holes at RHIC re-appeared today; for links you can follow Peter Steinberg's blog. For the record: the black holes being discussed are dual black holes, not "real" black holes. I would describe it this way: Via a mathematical "trick", one is able to make a QCD-like theory look like a classical theory of gravity in 10 dimensions. When one calculates black hole phenomena in that fictitious space, it turns out that they can be mapped directly onto QCD-like phenomena (such as quark-gluon plasma parameters) in the QCD-like theory. I have been careful to say "QCD-like", since this correspondence does not apply (directly) to "real" QCD.
To explain via an analogy: You probably know that a mathematical trick allows one to re-express the Schrodinger equation as a classical diffusion equation for (say) heat conduction. But this doesn't mean that the hydrogen atom is the same as a frying pan.
21-Mar-05: The next student-led session will be presented by Kerstin Perez on Tuesday, March 21st at 5:30 pm. Kerstin will discuss a paper aimed at calculating the production of real black holes in very high energy collisions (such as those the LHC will produce). Below is the reference, along with a couple of others.
28-Mar-05: The next student-led session will be presented by Jordan Horowitz on Tuesday, March 28th at 5:30 pm. Jordan will talk on "Universal Entropy Bound on Matter and an Introduction to the Holographic Principle". He has recommended the following paper on this topic:
Note that in Sections III and V this paper discussing the bounding of closed surfaces via null light-sheets, this is closely related to the material from last week that had me so puzzled.
Some additional information from Jordan:
06-Apr-05: The next student-led session will be presented by Maria Halmo on Wednesday, April 6th at 5:30 pm. Maria will talk about the need for general relativity in the Global Positioning System (GPS). Here are a couple of interesting links I found:
12-Apr-05: The next student-led session will be presented by Dhruv Bansal and Bill Pontius on Tuesday, April 12th at 5:30 pm. Here is the paper they will be presenting:
This is an introductory review of the AdS/CFT correspondence and of the ideas that led to its formulation. We show how comparison of stacks of D3-branes with corresponding supergravity solutions leads to dualities between conformal large $N$ gauge theories in 4 dimensions and string backgrounds of the form $AdS_5\times X_5$ where $X_5$ is an Einstein manifold. The gauge invariant chiral operators of the field theory are in one-to-one correspondence with the supergravity modes, and their correlation functions at strong `t Hooft coupling are determined by the dependence of the supergravity action on AdS boundary conditions. The simplest case is when $X_5$ is a 5-sphere and the dual gauge theory is the ${\cal N}=4$ supersymmetric SU(N) Yang-Mills theory. We also discuss D3-branes on the conifold corresponding to $X_5$ being a coset space $T^{1,1}=(SU(2)\times SU(2))/U(1)$. This background is dual to a certain ${\cal N}=1$ superconformal field theory with gauge group $SU(N)\times SU(N)$.
Also, as noted above, these lectures by Bigatti and Susskind may also provide an accessible introduction of AdS/CFT, holography and all that.
19-Apr-05: The next student-led session will be presented by Nada Petrovic on Tuesday, April 19th at 5:30 pm. Here is the paper she will discuss:
From: Steve Giddings [view email] Date: Mon, 28 Aug 95 11:50:06 PDT (16kb)
A concise survey of the black hole information paradox and its current status is given. A summary is also given of recent arguments against remnants. The assumptions underlying remnants, namely unitarity and causality, would imply that Reissner Nordstrom black holes have infinite internal states. These can be argued to lead to an unacceptable infinite production rate of such black holes in background fields. (To appear in the proceedings of the PASCOS symposium/Johns Hopkins Workshop, Baltimore, MD, March 22-25, 1995).