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

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

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Analogue Gravity Phenomenology : Analogue Spacetimes and Horizons, from Theory to Experiment
Title
Analogue Gravity Phenomenology
Title remainder
Analogue Spacetimes and Horizons, from Theory to Experiment
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eng
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MiAaPQ
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non fiction
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dictionaries
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Lecture Notes in Physics
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v.870
Analogue Gravity Phenomenology : Analogue Spacetimes and Horizons, from Theory to Experiment
Label
Analogue Gravity Phenomenology : Analogue Spacetimes and Horizons, from Theory to Experiment
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http://libproxy.rpi.edu/login?url=https://ebookcentral.proquest.com/lib/rpi/detail.action?docID=3093228
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online resource
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cr
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multicolored
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text
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txt
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rdacontent
Contents
  • Analogue Gravity Phenomenology -- Preface -- Contents -- Contributors -- Chapter 1: Black Holes and Hawking Radiation in Spacetime and Its Analogues -- 1.1 Spacetime Geometry and Black Holes -- 1.1.1 Spacetime Geometry -- 1.1.2 Spherical Black Hole -- 1.1.2.1 Schwarzschild Coordinates -- Redshift and Horizon -- 1.1.2.2 Painlevé-Gullstrand Coordinates -- 1.1.2.3 Spacetime Diagram of the Black Hole -- 1.1.2.4 Redshift of Outgoing Waves Near the Horizon -- 1.1.3 Effective Black Hole and White Hole Spacetimes -- Moving Texture -- Black Hole-White Hole Pair -- 1.1.4 Symmetries, Killing Vectors, and Conserved Quantities -- 1.1.4.1 Ergoregions -- 1.1.4.2 Conserved Quantities -- Killing Energy and Ergoregions -- 1.1.5 Killing Horizons and Surface Gravity -- Rindler (Acceleration) Horizon -- 1.1.5.1 Surface Gravity -- Surface Gravity of the Rindler Horizon -- 1.2 Thermality of the Vacuum -- 1.3 Hawking Effect -- 1.3.1 Mode Solutions -- 1.3.2 Positive Norm Modes and the Local Vacuum -- The Local Outgoing Vacuum -- 1.3.3 Stimulated Emission of Hawking Radiation -- 1.4 The Trans-Planckian Question -- 1.5 Short Wavelength Dispersion -- 1.5.1 Stimulated Hawking Radiation and Dispersion -- 1.5.2 White Hole Radiation -- References -- Chapter 2: Survey of Analogue Spacetimes -- 2.1 Introduction -- 2.2 Optics: The Gordon Metric and Its Generalizations -- Example -- Limitations -- Foreground-Background Version -- 2.3 Non-relativistic Acoustics: The Unruh Metric -- Geometric Acoustics -- Wave Acoustics -- 2.4 Horizons and Ergo-Surfaces in Non-relativistic Acoustics -- Stationary Versus Static -- Static Con gurations -- Stationary but Non-static Con gurations -- Stationary but Non-static Killing Horizons -- Stationary but Non-static Non-Killing Horizons -- 2.5 Relativistic Acoustics -- Geometric Acoustics -- Wave Acoustics -- Non-relativistic Limit
  • 2.6 Bose-Einstein Condensates -- Madelung Representation -- 2.7 Surface Waves and Blocking Horizons -- Surface Waves in the Geometric Limit -- Surface Waves in the Physical Limit -- Experiments -- 2.8 Optical Fibres/Optical Glass -- 2.9 Other Models -- 2.10 Discussion -- References -- Chapter 3: Cosmological Particle Creation in the Lab? -- 3.1 Introduction -- 3.2 Scattering Analogy -- 3.3 WKB Analysis -- 3.4 Adiabatic Expansion and Its Breakdown -- 3.5 Example: In ation -- 3.6 Laboratory Analogues -- References -- Chapter 4: Irrotational, Two-Dimensional Surface Waves in Fluids -- 4.1 Introduction -- 4.1.1 v0=0 Limit -- 4.1.2 Formal General Solution -- 4.2 Fluctuations -- 4.3 Shallow Water Waves -- 4.4 Deep Water Waves -- 4.5 General Linearized Waves -- 4.6 Blocking Flow -- 4.7 Conversion to deltay -- 4.8 Waves in Stationary Water over Uneven Bottom -- References -- Chapter 5: The Basics of Water Waves Theory for Analogue Gravity -- 5.1 Introduction -- 5.2 A Glimpse of Dimensional Analysis -- 5.2.1 Shallow Waters -- 5.2.2 Deep Waters -- 5.2.3 Arbitrary Water Depth -- 5.2.4 The Capillary Length -- 5.3 Long Water Waves on a Current as a Gravity Analogue -- 5.4 Fluid Particles' Trajectories -- 5.5 A Plethora of Dispersive Effects -- 5.6 Hydrodynamic Horizons -- 5.6.1 Non-dispersive Horizons -- 5.6.2 Dispersive Horizons -- 5.6.3 Natural and Arti cial Horizons -- 5.6.4 Zero Modes -- 5.6.4.1 The Zero Mode (Static Undulation) for Gravity Waves -- 5.6.4.2 The Zero Mode (Static Undulation) for Capillo-Gravity Waves -- 5.7 The "Norm" -- 5.8 Conclusion -- References -- Chapter 6: The Cerenkov Effect Revisited: From Swimming Ducks to Zero Modes in Gravitational Analogues -- 6.1 Introduction -- 6.2 Generic Model -- 6.2.1 The Wave Equation and the Source Term -- 6.2.2 Qualitative Geometrical Study of the Wake Pattern
  • 6.2.3 Generalization to Higher-Order Wave Equations -- 6.3 Cerenkov Emission by Uniformly Moving Charges -- 6.3.1 Non-dispersive Dielectric -- 6.4 Moving Impurities in a Super uid -- 6.4.1 The Bogoliubov Dispersion of Excitations -- 6.4.2 Super uidity vs. Bogoliubov-Cerenkov Wake -- 6.5 Parabolic Dispersion: Conics in the Wake -- 6.6 Surface Waves on a Liquid -- 6.6.1 Dispersion of Surface Waves -- 6.6.2 Deep Fluid -- 6.6.2.1 Fast Speed v»vmin (Deep Fluid, Negligible Surface Tension) -- 6.6.2.2 Moderate Speed v>̃vmin (Deep Fluid, Signi cant Surface Tension) -- 6.6.2.3 Effect of the Source Structure Factor -- 6.6.3 Shallow Fluid -- 6.6.3.1 Small Surface Tension (Sub-luminal Dispersion) -- 6.6.3.2 Shallow One-Dimensional Channel -- 6.6.3.3 Large Surface Tension (Super-luminal Dispersion) -- 6.7 Cerenkov Processes and the Stability of Analogue Black/White Holes -- 6.7.1 Super uid-Based Analogue Models -- 6.7.2 Analogue Models Based on Surface Waves -- 6.8 Conclusions -- References -- Chapter 7: Some Aspects of Dispersive Horizons: Lessons from Surface Waves -- 7.1 Introduction -- 7.2 Preliminaries -- 7.3 Experimental Setup -- 7.4 Experimental Results -- 7.5 Airy Interference and Gravity-Wave Blocking -- 7.6 The Trans-Planckian Problem -- Appendix: Airy Stopping Length -- References -- Chapter 8: Classical Aspects of Hawking Radiation Veri ed in Analogue Gravity Experiment -- 8.1 Motivation -- 8.2 Black & White Hole Evaporation Process -- 8.3 Experimental Setup -- 8.4 Quasi-Particle Excitations -- 8.5 Experimental Procedure -- 8.6 Data Analysis and Results -- 8.7 Conclusions and Outlook -- References -- Chapter 9: Understanding Hawking Radiation from Simple Models of Atomic Bose-Einstein Condensates -- 9.1 Introduction -- 9.2 The Theory of Dilute Bose-Einstein Condensates in a Nutshell -- 9.2.1 The Gross-Pitaevskii Equation and the Bogoliubov Theory
  • 9.2.2 Analogue Gravity in Atomic BECs -- 9.3 Stepwise Homogeneous Condensates -- 9.4 Subsonic-Subsonic Con guration -- 9.4.1 The Bogoliubov Modes and the Matching Matrix -- 9.4.2 The "In" and "Out" Basis -- 9.4.3 Bogoliubov Transformation -- 9.4.4 Density-Density Correlations -- 9.5 Subsonic-Supersonic Con guration -- 9.5.1 The Modes and the Matching Matrix -- 9.5.2 The "In" and "Out" Basis -- 9.5.3 Bogoliubov Transformation -- 9.5.4 Density-Density Correlations -- 9.5.5 Remarks -- 9.6 Supersonic-Supersonic Con guration -- 9.7 Conclusions -- Appendix -- References -- Chapter 10: Transformation Optics -- 10.1 Introduction -- 10.2 Maxwell's Electromagnetism -- 10.2.1 Maxwell's Equations -- 10.2.2 The Medium of a Geometry -- 10.2.3 The Geometry of a Medium -- 10.3 Spatial Transformations -- 10.3.1 Invisibility Cloaking -- 10.3.2 Transformation Media -- 10.3.3 Perfect Imaging with Negative Refraction -- 10.3.4 Quantum Levitation -- 10.4 Curved Space -- 10.4.1 Einstein's Universe and Maxwell's Fish Eye -- 10.4.2 Perfect Imaging with Positive Refraction -- 10.4.3 Casimir Force -- 10.5 Spacetime Media -- 10.5.1 Spacetime Geometries -- 10.5.2 Magneto-Electric Media -- 10.5.3 Moving Media -- 10.5.4 Spacetime Transformations -- References -- Chapter 11: Laser Pulse Analogues for Gravity -- 11.1 Introduction -- 11.1.1 White Holes -- 11.2 Analogue Gravity with Optics in Moving Media -- 11.3 Dielectric Metrics and Hawking Radiation -- 11.3.1 The Role of Dispersion -- 11.4 Numerical Simulations of One-Dimensional Dielectric White Holes -- 11.5 Stimulated Hawking Emission and Ampli cation -- 11.6 Creating an Effective Moving Medium with a Laser Pulse -- 11.7 Experiments: Spontaneous Emission from a Moving Perturbation -- 11.8 Conclusions and Perspectives -- References -- Chapter 12: An All-Optical Event Horizon in an Optical Analogue of a Laval Nozzle
  • 12.1 Introduction -- 12.2 Transonic Flow of a Luminous Fluid -- 12.3 An Experimental Horizon -- 12.4 Fluctuations -- 12.4.1 Classical Straddled Fluctuations -- 12.4.2 Regularization of Fluctuations Near the Mach Horizon -- 12.4.3 Quantization and the Hawking Temperature -- 12.5 Discussion -- 12.6 Summary -- References -- Chapter 13: Lorentz Breaking Effective Field Theory and Observational Tests -- 13.1 Introduction -- 13.2 A Brief History of an Heresy -- 13.2.1 The Dark Ages -- 13.2.2 Windows on Quantum Gravity -- 13.3 Bose-Einstein Condensates as an Example of Emergent Local Lorentz Invariance -- 13.3.1 The Acoustic Geometry in BEC -- 13.3.2 Lorentz Violation in BEC -- 13.4 Modi ed Dispersion Relations and Their Naturalness -- 13.4.1 The Naturalness Problem -- 13.4.1.1 A New Symmetry -- 13.4.1.2 Gravitational Con nement of Lorentz Violation -- 13.5 Dynamical Frameworks -- 13.5.1 SME with Renormalizable Operators -- 13.5.2 Dimension Five Operators SME -- 13.5.3 Dimension Six Operators SME -- 13.5.4 Other Frameworks -- 13.5.4.1 D-Brane Models -- 13.5.4.2 Doubly Special Relativity -- 13.6 Experimental Probes of Low Energy LV: Earth Based Experiments -- 13.6.1 Penning Traps -- 13.6.2 Clock Comparison Experiments -- 13.6.3 Cavity Experiments -- 13.6.4 Spin Polarized Torsion Balance -- 13.6.5 Neutral Mesons -- 13.7 Observational Probes of High Energy LV: Astrophysical QED Reactions -- 13.7.1 Photon Time of Flight -- 13.7.2 Vacuum Birefringence -- 13.7.3 Threshold Reactions -- 13.7.3.1 LV-Allowed Threshold Reactions: gamma-Decay -- 13.7.3.2 LV-Allowed Threshold Reactions: Vacuum Cerenkov and Helicity Decay -- 13.7.3.3 LV-Allowed Threshold Reactions: Photon Splitting and Lepton Pair Production -- Photon Splitting -- Lepton Pair Production -- 13.7.3.4 LV-Modi ed Threshold Reactions: Photon Pair-Creation -- 13.7.4 Synchrotron Radiation
  • 13.8 Current Constraints on the QED Sector
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