Bibliography: Analog models of General Relativity
Introduction:
This document is an attempt at a reasonably complete bibliography on analog methods.
Comments and suggestions should be sent to Matt Visser:
visser@mcs.vuw.ac.nz
Remember that analog methods can be used for at least three distinct purposes:
 To map general relativity into a condensed matter system; letting
you solve problems in general relativity by using a (hopefully)
conceptually simpler classical analog as a model.
(This is the most common approach.)
 To map condensed matter systems into general relativity, helping
you to clear up obscurities in condensed matter physics by using a
(hopefully) conceptually simpler general relativistic analog as a
model.
(See for instance the workshop contribution by Michael Stone
concerning the proper interpretation of momentum and pseudomomentum in
condensed matter physics.)
 To build models *for* general relativity (as opposed to models
*of* general relativity); this is useful if you view gravity as and
"effective theory" that is *not* fundamental. Then whatever the true
fundamental theory is it must have some subsector that adequately
reproduces most (if not all) of standard general relativity.
(See for instance instance the workshop contribution by Grigori
Volovik on using nonrelativistic quantum fermi liquids to provide
"induced gravity" [similar but not identical to Sakharov's "induced
gravity" proposal]. Also check the workshop contribution by Brandon
Carter on quasigravity versus pseudogravity.)
Because "analog models" means such different things to different
authors, and because many of the authors below worked in isolation
from the others, you may detect a certain lack of coherent viewpoint
in the papers cited below.
(In particular, the work initiated in the
1990's using analog models to probe the concept of Hawking radiation
was developed largely in ignorance of what had been done before.)
Warning: This bibliography is still rather fragmentary. It will
be extended and improved as time permits.
Historical period (Optics):
Perhaps the first paper to seriously discuss analog models and
effective metric techniques was that of Walther Gordon (yes, he of the
KleinGordon equation):
 W. Gordon
``Zur Lichtfortpflanzung nach der Relativitatstheorie''
Ann. Phys. Leipzig 72 (1923) 421456.
Note that Gordon seemed largely interested in trying to describe
dielectric media by an "effective metric". That is: Gordon wanted to
use a gravitational field to mimic a dielectric medium.
After that, there was sporadic interest in effective metric
techniques. One historically important contribution was one of the
*problems* in Landau and Lifshitz:
 L.D. Landau and E.M. Lifshitz
The classical theory of fields
See the end of chapter 10, paragraph 90, and the problem immediately thereafter:
"Equations of electrodynamics in the presence of a gravitational field".
Note that in contrast to Gordon, here the interest is in using
dielectric media to mimic a gravitational field.
In France the idea was taken up by Pham Mau Quan:

Sur les équations de l'electromagné dans la materie.
On the equations of electromagnetism in matter.
Note de M. Pham Mau Quan, presentée par M. G. Darmois
Note by Mr. Pham Mau Quan, presented by Mr. G. Darmois
Comptes R. Acad. Sciences 242, 465467 (Jan. 23 1956)
English Abstract:
Maxwell's equations can be expressed directly in the metric of the
coefficients
gamma_{alpha beta}=g_{alpha beta} [1 (1/lambda mu)]
u_{alpha} u_{beta},
which is obtained from the metric of the universe and the velocity
unit vector.
The trajectories of the electromagnetic rays are
interpreted in this case as geodesics of null length of this new
metric.
Three articles that directly used the dielectric analogy to analyze
specific physics problems are:
 G.V. Skrotskii
The influence of gravitation on the propagation of light.
Soviet Physics Doklady 2 (1957) 226229.
 N.L. Balazs
Effect of a gravitational field, due to a rotating body,
on the plane of polarization of an electromagnetic wave.
Physical Review 110 (1958) 236239.
 F. Winterberg
Detection of gravitational waves by stellar scintillation in space.
Il Nuovo Cimento 53B (1968) 264279.
This article studies the intensity fluctuations of light signals
in a medium of statistically distributed gravitational waves, and
shows that it is equivalent (or closely related) to the problem of
light signals in a refractive medium with statistically distributed
inhomogeneities.
See especially the optical metric at pp. 268269 and in the appendix.
The general formalism was more fully developed in articles such as:
 Jerzy Peblanski
Electromagnetic waves in gravitational fields
Physical Review 118 (1960) 13961408.
A good summary of this classical period is due to Fernando de Felice:
 F. de Felice
On the gravitational field acting as an optical medium
General Relativity and Gravitation 2 (1971) 347357.
In summary and with hindsight:
 An arbitrary gravitational field can always be represented as an
equivalent optical medium, but subject to the somewhat unphysical
restriction that [magnetic permitivity] = [electric permeability].
 If an optical medium does *not* satisfy [magnetic permitivity] =
[electric permeability] then it is not completely equivalent to a
gravitational field.
A complete equivalence can be established in the
geometric optics limit, but for wave optics the equivalence is not
complete.
Historical period (Acoustics):
There were several papers in the 1970's and 1980's using an acoustic
analogy to investigate the propagation of shockwaves in astrophysical
situations:
 V. Moncrief
Astrophysics J. 235 (1980) 1038.
(I have not been able to verify this reference.)
 Sabino Matarrese
Perturbations of an irrotational perfect fluid
Atti del VI convegno nazionale di relativita generale e fisica della gravitazione
(Firenze, 1013 ottobre 1984), pp 283287.
Proceedings of the 4'th Italian conference on general relativity and the physics of gravitation
(Florence, 1013 October 1984), pp 283287.
 Sabino Matarrese
Phonons in a relativistic perfect fluid
Proceedings of the 4'th Marcel Grossmann meeting on General Relativity,
R. Ruffini (ed.), (Elsevier, 1986), pp 15911595.
 Sabino Matarrese
On the classical and quantum irrotational motions of a relativistic perfect fluid . I. Classical Theory
Proc. R. Soc. Lond. A 401 (1985) 5366.
 Others?
(I have not been able to verify this reference.)
Recent period (Acoustics):
General Relativists refocussed interest in this topic after the key
paper of Unruh:
 W. G. Unruh
``Experimental black hole evaporation?''
Phys. Rev. Lett, 46, 13511353 (1981).
After a delay of another decade, Unruh's article lead to an explosion
of interest, with particular relevance to the Hawking radiation
process:
 T. Jacobson,
``Black hole evaporation and ultrashort distances''
Phys. Rev. D44, 1731 (1991).
 G. Comer,
``Superfluid analog of the DaviesUnruh effect''
August 1992 (unpublished).
 T. Jacobson,
``Black hole radiation in the presence of a short distance cutoff''
Phys. Rev. D48, 728 (1993) [hepth/9303103].
 M. Visser,
``Acoustic propagation in fluids: an unexpected example of Lorentzian geometry''
grqc/931102.
 W. G. Unruh,
``Dumb holes and the effects of high frequencies on black hole evaporation''
Phys. Rev. D51 (1995) 28272838 [grqc/9409008].
(Title changed in journal: ``Sonic analog of black holes and the effects of high frequencies on black hole evaporation'')
 D. Hochberg,
``Evaporating black holes and collapsing bubbles in fluids''
March 1997, (unpublished).
 M. Visser,
``Acoustic black holes: Horizons, ergospheres, and Hawking radiation''
Class. Quantum Grav. 15, 17671791 (1998) [grqc/9712010].
 S. Liberati, S. Sonego and M. Visser,
``Unexpectedly large surface gravities for acoustic horizons?''
Class. Quantum Grav. {17}, 29032923 (2000) [grqc/0003105].
 S. Liberati,
``Quantum vacuum effects in gravitational fields: Theory and detectability,''
Ph.D. thesis [grqc/0009050].
Recent period (Superfluids  Liquid Helium):
The use of superfluid systems, in particular liquid Helium, has been
extensively discussed by Volovik and coworkers:
 G. E. Volovik,
``Simulation of quantum field theory and gravity in superfluid ${}^3$He''
Low Temp. Phys. (Kharkov) 24,127129 (1998) [condmat/9706172].
 N. B. Kopnin and G. E. Volovik,
``Critical velocity and event horizon in paircorrelated systems with ``relativistic''
fermionic quasiparticles''
Pisma Zh. Eksp. Teor. Fiz. 67, 124129 (1998) [condmat/9712187].
 G. E. Volovik,
``Gravity of monopole and string and gravitational constant in ${}^3$HeA''
Pisma Zh. Eksp. Teor. Fiz. 67, 666671 (1998); JETP Lett. 67, 698704 (1998) [condmat/9804078].
 G. E. Volovik,
``Links between gravity and dynamics of quantum liquids''
[grqc/0004049].
 Title: Effective spacetime and Hawking radiation from moving domain wall in thin film of 3HeA
Author: T.A. Jacobson, G.E. Volovik
Journalref: Pisma Zh.Eksp.Teor.Fiz. 68 (1998) 833838; JETP Lett. 68 (1998) 874880
grqc/9811014; grqc@xxx.lanl.gov
 Title: Event horizons and ergoregions in 3He
Author: T.A. Jacobson, G.E. Volovik
Journalref: Phys.Rev.D 58, 064021 (1998)
condmat/9801308; condmat@xxx.lanl.gov
Recent period (Optical systems):
The use of "slow light" seems a
promising system for experimental implementation.
These are systems in which (over a limited range of frequencies) the
grouprefractiveindex is extremely high and the group velocity
extremely low
(though the phaserefractiveindex is unity and the
phase velocity is the usual speed of light).
Current [Y2K] experimental limits on the group velocity of light are
at the level of 50 centimetres/second.
 U. Leonhardt and P. Piwnicki
``Optics of nonuniformly moving media''
Phys. Rev. A 60, 43014312 (1999) [physics/9906038];
 U. Leonhardt and P. Piwnicki
``Relativistic effects of light in moving media with extremely low group velocity''
Phys. Rev. Lett. 84, 822825 (2000) [condmat/9906332].
 M. Visser,
``Comment on Relativistic effects of light in moving media with extremely low group velocity''
Phys. Rev. Lett. (in press), grqc/0002011.
 U. Leonhardt and P. Piwnicki,
``Reply to the Comment on Relativistic Effects of Light in Moving Media with Extremely Low Group Velocity''
Phys. Rev. Lett. (in press), grqc/0003016.
 Ulf Leonhardt
Spacetime geometry of quantum dielectrics
physics/0001064; physics@xxx.lanl.gov
physics/0001064
Physical Review A 62, 012111 (2000).
 Ultrahigh sensitivity of slowlight gyroscope
Authors: U. Leonhardt, P. Piwnicki
physics/0003092; physics@xxx.lanl.gov
Physical Review A 62, 055801 (2000)
 Slow light in moving media
Authors: U. Leonhardt and P. Piwnicki
physics/0009093; physics@xxx.lanl.gov
 Slowlight pulses in moving media
Authors: J. Fiurasek, U. Leonhardt, R. Parentani
quantph/0011100; quantph@xxx.lanl.gov
 Light propagation around a relativistic vortex flow of dielectric medium
Authors: B. Linet
grqc/0011018 ; grqc@xxx.lanl.gov
Recent period (BoseEinstein condensates):
The acoustic properties of BoseEinstein condensates are also of great
experimental interest. Sound velocities (propagation speeds for
perturbations in the phase of the condensate wavefunction) can be as
low as millimetres/second.
 L. J. Garay, J. R. Anglin, J. I. Cirac and P. Zoller,
``Black holes in BoseEinstein condensates''
Phys. Rev. Lett (in press), [grqc/0002015].
 L. J. Garay, J. R. Anglin, J. I. Cirac and P. Zoller,
``Sonic black holes in dilute BoseEinstein condensates''
Phys. Rev. A. (in press), [grqc/0005131].
 Carlos Barcelo, Stefano Liberati, and Matt Visser
``Analog gravity from BoseEinstein condensates''
grqc/0011026; grqc@xxx.lanl.gov
Recent period (Nonlinear electrodynamics):
Quantum corrections in QED lead to nonlinear electrodynamics:
electrodynamics that is not described by the usual Maxwell Lagrangian
but by the more general Schwinger Lagrangian (containing F^4 terms and
higher).
To lowest order in the fine structure, the Schwinger Lagrangian
reduces to the EulerHeisenberg Lagrangian.
Alternatively, by appealing to string theory, one can justify interest
in the BornInfeld Lagrangian.
All these examples of nonlinear electrodynamics lead to situations
where the propagation of photons can be described by looking at the
geodesics of an "effective metric" that is an algebraic function of
the background electromagnetic field. See:
 Jerzy Peblanski
Lectures on nonlinear electrodynamics
Nordita, Copenhagen, 1970.
 W. Dittrich and H. Gies,
``Light propagation in nontrivial QED vacua''
Phys. Rev. D 58, 025004 (1998) [hepph/9804375].
 M. Novello, V. A. De Lorenci, J. M. Salim and R. Klippert,
``Geometrical aspects of light propagation in nonlinear electrodynamics''
Phys. Rev. D 61, 045001 (2000) [grqc/9911085].
 M. Novello, V. A. De Lorenci, J. M. Salim and R. Klippert,
``Light propagation in nonlinear electrodynamics''
Phys. Lett. B482, 134140 (2000) [grqc/0005049].
 Stefano Liberati, Sebastiano Sonego and Matt Visser,
``Scharnhorst effect at oblique incidence''
quantph/0010055.
Recent period (Unclassified section):
A lot of relevant papers have appeared in the last 10 years or so
(19912000).
Sometimes it is a little difficult to classify them.
To be included below the paper must at least have something to say
about "effective metric" techniques.
That is, there should be some notion of an "effective metric",
physically distinct from the spacetime metric of general relativity,
that nevertheless influences the propagation of waves, signals, or
particles in some manner.
The references below still need to be ordered and categorized:
 T. Jacobson,
``TransPlanckian redshifts and the substance of the spacetime river''
Prog. Theor. Phys. Suppl. 136 (1999) 1 [hepth/0001085].
 B. Reznik,
``TransPlanckian tail in a theory with a cutoff''
Phys. Rev. D 55, 21522158 (1997); [grqc/9606083].
 B. Reznik,
``Origin of the thermal radiation in a solidstate analog of a black hole''
Phys. Rev. D 62, 0440441 (2000) [grqc/9703076].
 S. Corley and T. Jacobson,
``Hawking Spectrum and High Frequency Dispersion''
Phys. Rev. D54, 1568 (1996) [hepth/9601073].
 S. Corley,
``Particle creation via high frequency dispersion''
Phys. Rev. D55, 6155 (1997).
 S. Corley,
``Computing the spectrum of black hole radiation in the presence of high
frequency dispersion: An analytical approach''
Phys. Rev. D57, 6280 (1998) [hepth/9710075].
 T. Jacobson and D. Mattingly,
``Spontaneously broken Lorentz symmetry and gravity''
[grqc/0007031].
 Ted Jacobson and David Mattingly
``Hawking radiation on a falling lattice''
Journalref: Phys.Rev. D61 (2000) 024017
hepth/9908099
 T. Jacobson and D. Mattingly,
``Generally covariant model of a scalar field with high frequency
dispersion and the cosmological horizon problem''
[hepth/0009052].
 R. Brout, S. Massar, R. Parentani, Ph. Spindel,
``Hawking radiation without transplanckian frequencies''
Phys. Rev. D 52, 45594568 (1995); [hepth/9506121].
 T. Jacobson,
``Introduction to black hole microscopy''
published in Mexican School on Gravitation 1994, pages 87114, [hepth/9510026].
 T. Jacobson,
``On the origin of the outgoing black hole modes''
Phys. Rev. D 53, 70827088 (1996), hepth/9601064.
 S. Corley and T. Jacobson,
``Lattice black holes''
[hepth/9709166].
I do not claim to have an exhaustive bibliography.
Additional suggestions are welcome.
Extensive construction still in progress!
Last updated 28 November 2000
Comments to:
visser@mcs.vuw.ac.nz