Analogue Gravity Phenomenology: Analogue Spacetimes and Horizons, from Theory to Experiment

Summary

This volume provides a comprehensive overview and introduction to the field of analogue gravity, exploring the emulation of curved spacetime kinematics and astrophysical phenomena like Hawking radiation in diverse laboratory media. Topics covered include water wave dynamics, Bose-Einstein condensates, nonlinear optics, transformation optics, dispersion relations, and observational tests of Lorentz invariance violation. The collection serves as an interdisciplinary bridge linking general relativity, quantum field theory in curved spacetime, condensed matter physics, and fluid dynamics.

Front Matter & Title Page

Lecture Notes in Physics 870

Daniele Faccio · Francesco Belgiorno · Sergio Cacciatori · Vittorio Gorini · Stefano Liberati · Ugo Moschella (Editors)

Analogue Gravity Phenomenology Analogue Spacetimes and Horizons, from Theory to Experiment

Springer

Editorial Board & Publishing Information

Lecture Notes in Physics Volume 870

Founding Editors: W. Beiglböck, J. Ehlers, K. Hepp, H. Weidenmüller

Editorial Board: B.-G. Englert, Singapore, Singapore U. Frisch, Nice, France P. Hänggi, Augsburg, Germany W. Hillebrandt, Garching, Germany M. Hjort-Jensen, Oslo, Norway R. A. L. Jones, Sheffield, UK H. von Löhneysen, Karlsruhe, Germany M. S. Longair, Cambridge, UK M. L. Mangano, Geneva, Switzerland J.-F. Pinton, Lyon, France J.-M. Raimond, Paris, France A. Rubio, Donostia, San Sebastian, Spain M. Salmhofer, Heidelberg, Germany D. Sornette, Zurich, Switzerland S. Theisen, Potsdam, Germany D. Vollhardt, Augsburg, Germany W. Weise, Garching, Germany and Trento, Italy

For further volumes: www.springer.com/series/5304

Managing Editor at Springer: Christian Caron, Springer Heidelberg, Physics Editorial Department I, Tiergartenstrasse 17, 69121 Heidelberg/Germany, [email protected]

ISSN 0075-8450 | ISSN 1616-6361 (electronic) ISBN 978-3-319-00265-1 | ISBN 978-3-319-00266-8 (eBook) DOI 10.1007/978-3-319-00266-8 © Springer International Publishing Switzerland 2013

Preface

Reasoning by analogies is a natural inclination of the human brain that operates by associating new and unknown situations to a series of known and previously encountered situations… The purpose of this book is to give a general overview and introduction to the world of analogue gravity: the simulation or recreation of certain phenomena that are usually attributed to the effects of gravity but that can be shown to naturally emerge in a variety of systems ranging from flowing liquids to nonlinear optics.

Questions often arise regarding the implications of analogue models, particularly in the context of analogue gravity. The analogue models treated here can all be reconnected to some form of flowing medium reproducing or mimicking the flow of space generated by a gravitational field. The analogies reproduce to a large extent the kinematics of a black hole, determining photon or particle trajectories via the system’s spacetime metric. Bill Unruh first proposed an analogue for gravity in 1981 in the context of sound waves propagating in a flowing medium.

Table of Contents

1 Black Holes and Hawking Radiation in Spacetime and Its Analogues (Ted Jacobson) - 1 2 Survey of Analogue Spacetimes (Matt Visser) - 31 3 Cosmological Particle Creation in the Lab? (Ralf Schützhold and William G. Unruh) - 51 4 Irrotational, Two-Dimensional Surface Waves in Fluids (William G. Unruh) - 63 5 The Basics of Water Waves Theory for Analogue Gravity (Germain Rousseaux) - 81 6 The Čerenkov Effect Revisited: From Swimming Ducks to Zero Modes in Gravitational Analogues (Iacopo Carusotto and Germain Rousseaux) - 109 7 Some Aspects of Dispersive Horizons: Lessons from Surface Waves (Jennifer Chaline, Gil Jannes, Philippe Maïssa, and Germain Rousseaux) - 145 8 Classical Aspects of Hawking Radiation Verified in Analogue Gravity Experiment (Silke Weinfurtner, Edmund W. Tedford, Matthew C.J. Penrice, William G. Unruh, and Gregory A. Lawrence) - 167 9 Understanding Hawking Radiation from Simple Models of Atomic Bose-Einstein Condensates (Roberto Balbinot, Iacopo Carusotto, Alessandro Fabbri, Carlos Mayoral, and Alessio Recati) - 181 10 Transformation Optics (Ulf Leonhardt) - 221 11 Laser Pulse Analogues for Gravity (Eleonora Rubino, Francesco Belgiorno, Sergio Luigi Cacciatori, and Daniele Faccio) - 247 12 An All-Optical Event Horizon in an Optical Analogue of a Laval Nozzle (Moshe Elazar, Shimshon Bar-Ad, Victor Fleurov, and Rolf Schilling) - 275 13 Lorentz Breaking Effective Field Theory and Observational Tests (Stefano Liberati) - 297 14 The Topology of the Quantum Vacuum (Grigorii E. Volovik) - 343 15 Einstein²: Brownian Motion Meets General Relativity (Matteo Smerlak) - 385 16 Astrophysical Black Holes: Evidence of a Horizon? (Monica Colpi) - 399 Index - 437

Chapter 1: Black Holes and Hawking Radiation in Spacetime and Its Analogues

Author: Ted Jacobson Abstract: These notes introduce the fundamentals of black hole geometry, the thermality of the vacuum, and the Hawking effect, in spacetime and its analogues. Stimulated emission of Hawking radiation, the trans-Planckian question, short wavelength dispersion, and white hole radiation in the setting of analogue models are also discussed. No prior knowledge of differential geometry, general relativity, or quantum field theory in curved spacetime is assumed. Key topics include: Spacetime geometry and line elements; Schwarzschild coordinates and gravitational redshift; Painlevé-Gullstrand coordinates; effective black hole and white hole spacetimes (metric form ds² = c(x)² dt² - [dx - v(x)dt]²); Killing vectors, conserved quantities, ergoregions, and surface gravity; thermality of the Rindler vacuum; mode solutions across horizons; and short wavelength dispersion as a resolution to the trans-Planckian problem.

Chapter 2: Survey of Analogue Spacetimes

Author: Matt Visser Abstract: Analogue spacetimes provide concrete physical models to analyze excitation propagation using the mathematical tools of differential geometry. This chapter surveys fundamental analogue models including the Gordon optical metric (1923), non-relativistic acoustics and the Unruh metric (1981), acoustic horizons and ergosurfaces, relativistic acoustics, Bose-Einstein condensates, surface waves with blocking horizons, and optical fibre refractive index pulses (RIPs).

Chapter 3: Cosmological Particle Creation in the Lab?

Authors: Ralf Schützhold and William G. Unruh Abstract: Reviews cosmological particle creation from the quantum vacuum due to cosmic expansion or contraction. Discusses the mapping to one-dimensional Schrödinger scattering problems, WKB analysis, the breakdown of adiabatic expansion, applications to cosmic inflation (scale invariance of perturbations), and experimental laboratory analogue proposals utilizing time-dependent media or trapped ions.

Chapter 4: Irrotational, Two-Dimensional Surface Waves in Fluids

Author: William G. Unruh Abstract: Derives equations for surface waves on an irrotational incompressible fluid using velocity potential/stream function coordinates. Explores both shallow and deep water wave approximations over variable bottom topographies, blocking flows, and the conserved norm for surface waves essential for canonical quantization in analogue gravity experiments.

Chapter 5: The Basics of Water Waves Theory for Analogue Gravity

Author: Germain Rousseaux Abstract: Introduces water wave propagation on background flows, dimensional analysis, shallow/deep water regimes, capillary effects, hydrodynamic horizons (dispersive vs. non-dispersive), and zero modes (static undulations/hydraulic jumps). Establishes that the conserved ‘norm’ in analogue models corresponds to classical wave action.

Chapter 6: The Čerenkov Effect Revisited: From Swimming Ducks to Zero Modes in Gravitational Analogues

Authors: Iacopo Carusotto and Germain Rousseaux Abstract: Reviews generalized Čerenkov radiation across classical electromagnetism, superfluid hydrodynamics, and surface gravity waves. Details the geometric construction linking dispersion relation geometries Ω(k) = k·v to real-space Mach cones, Bogoliubov-Čerenkov wakes, Kelvin ship waves, and zero-mode emission affecting horizon stability in analogue black/white holes.

Chapter 7: Some Aspects of Dispersive Horizons: Lessons from Surface Waves

Authors: Jennifer Chaline, Gil Jannes, Philippe Maïssa, Germain Rousseaux Abstract: Investigates gravity-capillary surface waves encountering counter-currents. Explores white-hole horizons, blue horizons, Airy interference stopping lengths, dispersive horizon penetration, and implications for addressing the trans-Planckian problem in quantum gravity.

Chapter 8: Classical Aspects of Hawking Radiation Verified in Analogue Gravity Experiment

Authors: Silke Weinfurtner, Edmund W. Tedford, Matthew C.J. Penrice, William G. Unruh, Gregory A. Lawrence Abstract: Presents experimental verification of stimulated Hawking emission at a hydrodynamic white hole horizon in a water flume tank. Demonstrates pair-wave mode conversion into positive and negative norm states governed by a thermal Boltzmann distribution scaling with the flow velocity gradient.

Chapter 9: Understanding Hawking Radiation from Simple Models of Atomic Bose-Einstein Condensates

Authors: Roberto Balbinot, Iacopo Carusotto, Alessandro Fabbri, Carlos Mayoral, Alessio Recati Abstract: Uses Bogoliubov-de Gennes microscopic theory on a piecewise uniform 1D condensate to analytically derive spontaneous phonon emission by an acoustic horizon. Discusses S-matrix matching, positive/negative norm mode mixing, thermal spectra, and density-density correlation signatures.

Chapter 10: Transformation Optics

Author: Ulf Leonhardt Abstract: Reviews transformation optics, mapping coordinate transformations to anisotropic impedance-matched media. Explores invisibility cloaking, perfect lenses via negative refraction, Casimir force manipulation, Maxwell’s fish-eye lens, and optical event horizons generated by moving refractive index perturbations.

Chapter 11: Laser Pulse Analogues for Gravity

Authors: Eleonora Rubino, Francesco Belgiorno, Sergio Luigi Cacciatori, Daniele Faccio Abstract: Analyzes ultrashort laser pulses in nonlinear Kerr media generating moving refractive index perturbations (effective Gordon metrics). Discusses black/white hole horizon conditions, stimulated and spontaneous Hawking emission, dispersion effects, and experimental detection at 90 degrees.

Chapter 12: An All-Optical Event Horizon in an Optical Analogue of a Laval Nozzle

Authors: Moshe Elazar, Shimshon Bar-Ad, Victor Fleurov, Rolf Schilling Abstract: Demonstrates an all-optical event horizon using laser beam propagation in a nonlinear defocusing waveguide mimicking an aerodynamic Laval nozzle. Analyzes classical straddled fluctuations, quantum potential regularization, and effective Hawking temperature.

Chapter 13: Lorentz Breaking Effective Field Theory and Observational Tests

Author: Stefano Liberati Abstract: Reviews the Standard Model Extension (SME) and effective field theory approaches to Lorentz invariance violation (LV). Examines theoretical frameworks (SUSY, Hořava-Lifshitz gravity), laboratory tests (clocks, Penning traps), and astrophysical constraints from high-energy cosmic rays, Crab Nebula synchrotron/birefringence data, and neutrino observations.

Chapter 14: The Topology of the Quantum Vacuum

Author: Grigorii E. Volovik Abstract: Explores momentum-space topology as the classifying principle of the quantum vacuum. Analyzes Fermi surfaces, Weyl points, emergent Lorentz invariance, gauge/gravity fields, topological insulators, and superfluid ³He-A and ³He-B phases.

Chapter 15: Einstein²: Brownian Motion Meets General Relativity

Author: Matteo Smerlak Abstract: Blends general relativity with Brownian motion theory, showing how gravitational curvature and redshift alter diffusion equations and mean-square displacement. Discusses tailored diffusion in analogue metamaterials, antidiffusion, and relative entropy in non-equilibrium thermodynamics.

Chapter 16: Astrophysical Black Holes: Evidence of a Horizon?

Author: Monica Colpi Abstract: Reviews observational evidence for stellar-mass and supermassive astrophysical black holes. Discusses mass limits (Oppenheimer-Volkoff), accretion disc physics, spin measurement techniques (continuum fitting and Fe Kα line broadening), and future tests of Kerr geometry with gravitational wave observatories (eLISA/EMRIs).