One Hundred Years of General Relativity: From Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity (The 2 Volumes)

Volume 1
Foreword v
Color plates I-CP1
Part I. Genesis, Solutions and Energy I-1
1. A genesis of special relativity I-3
Val´erie Messager and Christophe Letellier
IJMPD 24 (2015) 1530024
1. Introduction I-3
2. The Ether: From Celestial Body Motion to Light
Propagation I-5
2.1. Its origin I-5
2.2. The luminiferous ether I-8
3. Galileo’s Composition Law for Velocities I-11
4. Questioning the Nature of Light: Waves
or Corpuscles? I-15
5. From Electrodynamics to Light I-24
5.1. Amp`ere’s law I-24
5.2. Maxwell’s electromagnetic waves as light I-28
5.3. Helmholtz’s theory I-32
5.4. Hertzs experiments for validating Maxwell’s
theory I-33
6. Invariance of the Field Equations from a Frame
to Another One I-37
6.1. Hertz’s electrodynamic theory I-37
6.2. Voigt’s wave equation I-41
6.3. Lorentz’s electrodynamical theory I-42
6.4. Larmor’s theory I-50
7. Poincar´e’s Contribution I-51
8. Einstein’s 1905 Contribution I-72
9. Conclusion I-76
Appendices I-77
A. 1. Fizeau’s experiments I-77
xi
xii Contents
A. 2. Michelson and Morley’s experiments I-77
2. Genesis of general relativity — A concise exposition I-85
Wei-Tou Ni
IJMPD 25 (2016) 1630004
1. Prelude — Before 1905 I-86
2. The Period of Searching for Directions and New
Ingredients: 1905–1910 I-91
3. The Period of Various Trial Theories: 1911–1914 I-96
4. The Synthesis and Consolidation: 1915–1916 I-100
5. Epilogue I-103
3. Schwarzschild and Kerr solutions of Einstein’s field
equation: An Introduction I-109
Christian Heinicke and Friederich W. Hehl
IJMPD 24 (2015) 1530006
1. Prelude I-109
1.1. Newtonian gravity I-109
1.2. Minkowski space I-114
1.2.1. Null coordinates I-115
1.2.2. Penrose diagram I-115
1.3. Einstein’s field equation I-118
2. The Schwarzschild Metric (1916) I-120
2.1. Historical remarks I-120
2.2. Approaching the Schwarzschild metric I-122
2.3. Six classical representations of the
Schwarzschild metric I-126
2.4. The concept of a Schwarzschild black hole I-126
2.4.1. Event horizon I-128
2.4.2. Killing horizon I-130
2.4.3. Surface gravity I-131
2.4.4. Infinite redshift I-131
2.5. Using light rays as coordinate lines I-131
2.5.1. Eddington–Finkelstein coordinates I-132
2.5.2. Kruskal–Szekeres coordinates I-133
2.6. Penrose–Kruskal diagram I-135
2.7. Adding electric charge and the cosmological
constant: Reissner–Nordstr¨om I-136
2.8. The interior Schwarzschild solution and the
TOV equation I-137
Contents xiii
3. The Kerr Metric (1963) I-141
3.1. Historical remarks I-141
3.2. Approaching the Kerr metric I-144
3.2.1. Papapetrou line element and vacuum
field equation I-144
3.2.2. Ernst equation (1968) I-147
3.2.3. From Ernst back to Kerr I-148
3.3. Three classical representations of the
Kerr metric I-149
3.4. The concept of a Kerr black hole I-151
3.4.1. Depicting Kerr geometry I-152
3.5. The ergoregion I-155
3.5.1. Constrained rotation I-155
3.5.2. Rotation of the event horizon I-156
3.5.2. Penrose process and black hole
thermodynamics I-156
3.6. Beyond the horizons I-157
3.6.1. Using light rays as coordinate lines I-158
3.7. Penrose–Carter diagram and Cauchy horizon I-160
3.8. Gravitoelectromagnetism, multipole moments I-161
3.8.1. Gravitoelectromagnetic field strength I-163
3.8.2. Quadratic invariants I-165
3.8.3. Gravitomagnetic clock effect of
Mashhoon, Cohen et al. I-166
3.8.4. Multipole moments: Gravitoelectric
and gravitomagnetic ones I-167
3.9. Adding electric charge and the cosmological
constant: Kerr–Newman metric I-168
3.10. On the uniqueness of the Kerr black hole I-170
3.11. On interior solutions with material sources I-171
4. Kerr Beyond Einstein I-172
4.1. Kerr metric accompanied by a propagating
linear connection I-172
4.2. Kerr metric in higher dimensions and
in string theory I-174
Appendix I-175
A.1. Exterior calculus and computer algebra I-175
xiv Contents
4. Gravitational energy for GR and Poincar´e
gauge theories: A covariant Hamiltonian approach I-187
Chiang-Mei Chen, James Nester and Roh-Suan Tung
IJMPD 24 (2015) 1530026
1. Introduction I-188
2. Background I-189
2.1. Some brief early history I-189
2.2. From Einstein’s correspondence I-190
2.3. Noether’s contribution I-192
2.4. Noether’s result I-193
3. The Noether Energy–Momentum Current
Ambiguity I-194
4. Pseudotensors I-196
4.1. Einstein, Klein and superpotentials I-197
4.2. Other GR pseudotensors I-198
4.3. Pseudotensors and the Hamiltonian I-200
5. The Quasi-Local View I-201
6. Currents as Generators I-201
7. Gauge and Geometry I-202
8. Dynamical Spacetime Geometry and the
Hamiltonian I-203
8.1. Pseudotensors and the Hamiltonian I-204
8.2. Some comments I-204
9. Differential Forms I-204
10. Variational Principle for Form Fields I-206
10.1. Hamiltons principle I-207
10.2. Compact representation I-207
11. Some Simple Examples of the Noether Theorems I-208
11.1. Noether’s first theorem: Energy–momentum I-208
11.2. Noether’s second theorem: Gauge fields I-209
11.3. Field equations with local gauge theory I-211
12. First-Order Formulation I-213
13. The Hamiltonian and the 3 + 1 Spacetime Split I-214
13.1. Canonical Hamiltonian formalism I-215
13.2. The differential form of the spacetime
decomposition I-215
13.3. Spacetime decomposition of the variational
formalism I-217
Contents xv
14. The Hamiltonian and Its Boundary Term I-218
14.1. The translational Noether current I-219
14.2. The Hamiltonian formulation I-220
14.3. Boundary terms: The boundary condition
and reference I-221
14.4. Covariant-symplectic Hamiltonian
boundary terms I-222
15. Standard Asymptotics I-223
15.1. Spatial infinity I-224
15.2. Null infinity I-224
15.3. Energy flux I-225
16. Application to Electromagnetism I-225
17. Geometry: Covariant Differential Formulation I-227
17.1. Metric and connection I-228
17.2. Riemann–Cartan geometry I-229
17.3. Regarding geometry and gauge I-230
17.4. On the affine connection and gauge theory I-230
18. Variational Principles for Dynamic Spacetime
Geometry I-232
18.1. The Lagrangian and its variation I-232
18.2. Local gauge symmetries, Noether currents
and differential identities I-233
18.3. Interpretation of the differential identities I-238
19. First-Order Form and the Hamiltonian I-240
19.1. First-order Lagrangian and local gauge
symmetries I-240
19.2. Generalized Hamiltonian and differential
identities I-241
19.3. General geometric Hamiltonian boundary
terms I-244
19.4. Quasi-local boundary terms I-245
19.5. A preferred choice I-245
19.6. Einstein’s GR I-246
19.7. Preferred boundary term for GR I-247
20. A “Best Matched” Reference I-248
20.1. The choice of reference I-249
20.2. Isometric matching of the 2-surface I-250
20.3. Complete 4D isometric matching I-251
xvi Contents
20.4. Complete 4D isometric matching I-251
21. Concluding Discussion I-252
Part II. Empirical Foundations I-263
5. Equivalence principles, spacetime structure
and the cosmic connection I-265
Wei-Tou Ni
IJMPD 25 (2016) 1630002
1. Introduction I-265
2. Meaning of Various Equivalence Principles I-270
2.1. Ancient concepts of inequivalence I-271
2.2. Macroscopic equivalence principles I-271
2.3. Equivalence principles for photons
(wave packets of light) I-273
2.4. Microscopic equivalence principles I-273
2.5. Equivalence principles including gravity
(Strong equivalence principles) I-276
2.6. Inequivalence and interrelations of various
equivalence principles I-277
3. Gravitational Coupling to Electromagnetism and
the Structure of Spacetime I-278
3.1. Premetric electrodynamics as a framework
to study gravitational coupling
to electromagnetism I-278
3.2. Wave propagation and the dispersion relation I-279
3.2.1. The condition of vanishing of
B(1) and B(2) for all directions of
wave propagation I-282
3.2.2. The condition of
(Sk)B(1) =(P)B(1) =0 and A(1) = A(2)
for all directions of wave propagation I-284
3.3. Nonbirefringence condition for the
skewonless case I-284
3.4. Wave propagation and the dispersion
relation in dilaton field and axion field I-288
3.5. No amplification/no attenuation and
no polarization rotation constraints
on cosmic dilaton field and cosmic axion field I-292
3.6. Spacetime constitutive relation including
skewons I-293
Contents xvii
3.7. Constitutive tensor from asymmetric metric
and Fresnel equation I-297
3.8. Empirical foundation of the closure relation
for skewonless case I-300
4. From Galileo Equivalence Principle to Einstein
Equivalence Principle I-303
5. EEP and Universal Metrology I-305
6. Gyrogravitational Ratio I-307
7. An Update of Search for Long Range/Intermediate
Range Spin–Spin, Spin–Monopole and
Spin–Cosmos Interactions I-308
8. Prospects I-309
6. Cosmic polarization rotation: An astrophysical test
of fundamental physics I-317
Sperello di Serego Alighieri
IJMPD 24 (2015) 1530016
1. Introduction I-317
2. Impact of CPR on Fundamental Physics I-318
3. Constraints from the Radio Polarization of RGs I-319
4. Constraints from the UV Polarization of RGs I-320
5. Constraints from the Polarization of the
CMB Radiation I-321
6. Other Constraints I-325
7. Discussion I-326
8. Outlook I-327
7. Clock comparison based on laser ranging technologies I-331
´Etienne Samain
IJMPD 24 (2015) 1530021
1. Introduction I-331
2. Scientific Objectives I-335
2.1. Time and frequency metrology I-335
2.2. Fundamental physics I-338
2.3. Solar System science I-340
2.4. Solar System navigation based on clock
comparison I-341
3. Time Transfer by Laser Link: T2L2 on Jason-2 I-341
3.1. Principle I-341
3.2. Laser station ground segment I-342
xviii Contents
3.3. Space instrument I-344
3.4. Time equation I-347
3.5. Error budget I-349
3.6. Link budget I-351
3.7. Exploitation I-352
4. One-Way Lunar Laser Link on LRO Spacecraft I-357
5. Prospective I-361
6. Conclusion and Outlook I-364
8. Solar-system tests of relativistic gravity I-371
Wei-Tou Ni
IJMPD 25 (2016) 1630003
1. Introduction and Summary I-371
2. Post-Newtonian Approximation, PPN Framework,
Shapiro Time Delay and Light Deflection I-374
2.1. Post-Newtonian approximation I-375
2.2. PPN framework I-377
2.3. Shapiro time delay I-380
2.4. Light deflection I-381
3. Solar System Ephemerides I-382
4. Solar System Tests I-385
5. Outlook — On Going and Next-Generation Tests I-393
9. Pulsars and gravity I-407
R. N. Manchester
IJMPD 24 (2015) 1530018
1. Introduction I-407
1.1. Pulsar timing I-410
2. Tests of Relativistic Gravity I-412
2.1. Tests of general relativity with
double-neutron-star systems I-412
2.1.1. The Hulse–Taylor binary, PSR
B1913+16 I-412
2.1.2. PSR B1534+12 I-415
2.1.3. The double pulsar, PSR
J0737−3039A/B I-417
2.1.4. Measured post-Keplerian parameters I-421
2.2. Tests of equivalence principles and
alternative theories of gravitation I-421
2.2.1. Limits on PPN parameters I-423
Contents xix
2.2.2. Dipolar gravitational waves and the
constancy of G I-427
2.2.3. General scalar–tensor and
scalar–vector–tensor theories I-429
2.3. Future prospects I-431
3. The Quest for Gravitational-Wave Detection I-432
3.1. Pulsar timing arrays I-432
3.2. Nanohertz gravitational-wave sources I-435
3.2.1. Massive black-hole binary systems I-435
3.2.2. Cosmic strings and the early universe I-439
3.2.3. Transient or burst GW sources I-440
3.3. Pulsar timing arrays and current results I-443
3.3.1. Existing PTAs I-444
3.3.2. Limits on the nanohertz GW
background I-445
3.3.3. Limits on GW emission from
individual black-hole binary systems I-446
3.4. Future prospects I-450
4. Summary and Conclusion I-452
Part III. Gravitational Waves I-459
10. Gravitational waves: Classification, methods
of detection, sensitivities, and sources I-461
Kazuaki Kuroda, Wei-Tou Ni and Wei-Ping Pan
IJMPD 24 (2015) 1530031
1. Introduction and Classification I-461
2. GWs in GR I-464
3. Methods of GW Detection, and Their Sensitivities I-470
3.1. Sensitivities I-471
3.2. Very high frequency band
(100kHz–1THz) and ultrahigh
frequency band (above 1THz) I-477
3.3. High frequency band (10Hz–100kHz) I-478
3.4. Doppler tracking of spacecraft (1 μHz–1mHz
in the low-frequency band) I-480
3.5. Space interferometers (low-frequency band,
100 nHz–100mHz; middle-frequency band,
100mHz–10Hz) I-481
3.6. Very-low-frequency band (300 pHz–100 nHz) I-486
3.7. Ultra-low-frequency band (10 fHz–300 pHz) I-488
xx Contents
3.8. Extremely-low (Hubble)-frequency band
(1 aHz–10 fHz) I-489
4. Sources of GWs I-491
4.1. GWs from compact binaries I-491
4.2. GWs from supernovae I-492
4.3. GWs from massive black holes and their
coevolution with galaxies I-493
4.4. GWs from extreme mass ratio inspirals (EMRIs) I-495
4.5. Primordial/inflationary/relic GWs I-495
4.6. Very-high-frequency and ultra-high-frequency
GW sources I-496
4.7. Other possible sources I-496
5. Discussion and Outlook I-497
11. Ground-based gravitational-wave detectors I-505
Kazuaki Kuroda
IJMPD 24 (2015) 1530032
1. Introduction to Ground-Based Gravitational-Wave
Detectors I-505
1.1. Gravitational-wave sources I-506
1.1.1. Achieved sensitivities of large projects I-506
1.1.2. Coalescences of binary neutron stars I-508
1.1.3. Coalescences of binary black holes I-508
1.1.4. Supernova explosion I-509
1.1.5. Quasi-normal mode oscillation at the
birth of black hole I-509
1.1.6. Unstable fast rotating neutron star I-510
1.2. Acceleration due to a gravitational wave I-510
1.3. Response of a resonant antenna I-512
1.4. Response of a resonant antenna I-515
1.4.1. Directivity I-516
1.4.1. Positioning I-518
1.5. Comparison of a resonant antenna and
an interferometer I-519
2. Resonant Antennae I-519
2.1. Development of resonant antennae I-520
2.2. Dynamical model of a resonant antenna with
two modes I-523
2.3. Signal-to-noise ratio and noise temperature I-525
Contents xxi
2.4. Comparison of five resonant antennae I-526
3. Interferometers I-527
3.1. First stage against technical noises
in prototype interferometers I-528
3.1.1. 3m-Garching interferometer I-528
3.1.2. 30m-Garching interferometer I-530
3.1.3. Glasgow 10m-Fabry–Perot Michelson
interferometer I-533
3.1.4. Caltech 40m-Fabry–Perot Michelson
interferometer I-535
3.1.5. ISAS 10m and 100m delay-line
interferometer I-536
3.2. Further R&D efforts in the first-generation
detectors I-536
3.2.1. Power recycling I-537
3.2.2. Signal recycling and resonant
side-band extraction I-538
3.3. Fighting with thermal noise of the second stage I-539
3.3.1. Mirror and suspension thermal noise I-540
3.3.2. Thermal noise of optical coating I-542
3.4. Fighting against quantum noises and squeezing I-543
3.4.1. Radiation pressure noise I-543
3.4.2. Squeezing I-544
4. Large Scale Projects I-546
4.1. LIGO project I-546
4.2. Virgo project I-548
4.3. GEO project I-552
4.4. TAMA/CLIO/LCGT(KAGRA) project I-555
4.4.1. TAMA I-555
4.4.2. CLIO I-558
4.4.3. LCGT (KAGRA) I-561
4.4.4. Einstein telescope I-565
5. Summary I-566
Appendix A. Thermal Noise I-567
A.1. Nyquist theorem I-567
A.2. Thermal noise of a harmonic oscillator I-568
Appendix B. Modulation I-569
Appendix C. Fabry–Perot Interferometer I-571
xxii Contents
C.1. Fabry–Perot cavity I-571
C.2. Frequency response of a Fabry–Perot Michelson
interferometer I-572
Appendix D. Newtonian Noise I-573
12. Gravitational wave detection in space I-579
Wei-Tou Ni
IJMPD 25 (2016) 1630001
1. Introduction I-579
2. Gravity and Orbit Observations/Experiments
in the Solar System I-586
3. Doppler Tracking of Spacecraft I-589
4. Interferometric Space Missions I-591
5. Frequency Sensitivity Spectrum I-596
6. Scientific Goals I-601
6.1. Massive black holes and their co-evolution
with galaxies I-601
6.2. Extreme mass ratio inspirals I-603
6.3. Testing relativistic gravity I-603
6.4. Dark energy and cosmology I-603
6.5. Compact binaries I-604
6.6. Relic GWs I-604
7. Basic Orbit Configuration, Angular Resolution
and Multi-Formation Configurations I-605
7.1. Basic LISA-like orbit configuration I-605
7.2. Basic ASTROD orbit configuration I-607
7.3. Angular resolution I-611
7.4. Six/twelve spacecraft formation I-612
8. Orbit Design and Orbit Optimization Using
Ephemerides I-612
8.1. CGC ephemeris I-613
8.2. Numerical orbit design and orbit
optimization for eLISA/NGO I-614
8.3. Orbit optimization for ASTROD-GW I-616
8.3.1. CGC 2.7.1 ephemeris I-616
8.3.2. Initial choice of spacecraft initial
conditions I-616
8.3.3. Method of optimization I-617
9. Deployment of Formation in Earthlike Solar Orbit I-619
10. Time Delay Interferometry I-619
Contents xxiii
11. Payload Concept I-622
12. Outlook I-624
Subject Index I
Author Index XIII
Volume 2
Foreword v
Color plates II-CP1
Part IV. Cosmology II-1
13. General Relativity and Cosmology II-3
Martin Bucher and Wei-Tou Ni
IJMPD 24 (2015) 1530030
14. Cosmic Structure II-19
Marc Davis
IJMPD 23 (2014) 1430021
1. History of Cosmic Discovery II-19
2. Measurement of the Galaxy Correlation Function II-22
2.1. Before 1980 II-22
2.2. After 1980 II-23
2.3. Remarkable large-scale structure in simulations II-25
2.4. Measurement of the BAO effect II-26
2.5. Further measurements of the power spectrum II-28
2.6. Lyman-α clouds II-29
3. Large Scale Flows II-31
4. Dwarf Galaxies as a Probe of Dark Matter II-34
5. Gravitational Lensing II-38
5.1. Double images II-38
5.2. Bullet cluster II-38
5.3. Substructure of gravitational lenses II-38
6. Conclusion II-40
15. Physics of the cosmic microwave background anisotropy II-43
Martin Bucher
IJMPD 24 (2015) 1530004
1. Observing the Microwave Sky: A Short History
and Observational Overview II-43
2. Brief Thermal History of the Universe II-54
xxiv Contents
3. Cosmological Perturbation Theory: Describing
a Nearly Perfect Universe Using General Relativity II-58
4. Characterizing the Primordial Power Spectrum II-61
5. Recombination, Blackbody Spectrum, and
Spectral Distortions II-62
6. Sachs–Wolfe Formula and More Exact Anisotropy
Calculations II-63
7. What CanWe Learn From the CMB Temperature
and Polarization Anisotropies? II-69
7.1. Character of primordial perturbations:
Adiabatic growing mode versus field ordering II-69
7.2. Boltzmann hierarchy evolution II-71
7.3. Angular diameter distance II-76
7.4. Integrated Sachs–Wolfe effect II-77
7.5. Reionization II-78
7.6. What we have not mentioned II-83
8. Gravitational Lensing of the CMB II-84
9. CMB Statistics II-86
9.1. Gaussianity, non-Gaussianity, and all that II-86
9.2. Non-Gaussian alternatives II-92
10. Bispectral Non-Gaussianity II-92
11. B Modes: A New Probe of Inflation II-94
11.1. Suborbital searches for primordial B modes II-95
11.2. Space based searches for primordial B modes II-96
12. CMB Anomalies II-96
13. Sunyaev–Zeldovich Effects II-98
14. Experimental Aspects of CMB Observations II-100
14.1. Intrinsic photon counting noise: Ideal
detector behavior II-102
14.2. CMB detector technology II-104
14.3. Special techniques for polarization II-106
15. CMB Statistics Revisited: Dealing with Realistic
Observations II-110
16. Galactic Synchrotron Emission II-112
17. Free–Free Emission II-113
18. Thermal Dust Emission II-114
19. Dust Polarization and Grain Alignment II-116
19.1. Why do dust grains spin? II-117
Contents xxv
19.2. About which axis do dust grains spin? II-118
19.3. A stochastic differential equation for L(t) II-118
19.4. Suprathermal rotation II-119
19.5. Dust grain dynamics and the galactic
magnetic field II-120
19.5.1. Origin of a magnetic moment along L II-121
19.6. Magnetic precession II-122
19.6.1. Barnett dissipation II-122
19.7. Davis–Greenstein magnetic dissipation II-124
19.8. Alignment along B without
Davis–Greenstein dissipation II-125
19.9. Radiative torques II-126
19.10. Small dust grains and anomalous
microwave emission (AME) II-128
20. Compact Sources II-130
20.1. Radio galaxies II-131
20.2. Infrared galaxies II-132
21. Other Effects II-132
21.1. Patchy reionization II-132
21.2. Molecular lines II-132
21.3. Zodiacal emission II-133
22. Extracting the Primordial CMB Anisotropies II-133
23. Concluding Remarks II-134
16. SNe Ia as a cosmological probe II-151
Xiangcun Meng, Yan Gao and Zhanwen Han
IJMPD 24 (2015) 1530029
1. Introduction II-151
2. SNe Ia as a Standardizable Distance Candle II-152
3. Progenitors of SNe Ia II-157
4. Effect of SN Ia Populations on Their Brightness II-160
5. SN Ia’s Role in Cosmology II-163
6. Issues and Prospects II-167
17. Gravitational Lensing in Cosmology II-173
Toshifumi Futamase
IJMPD 24 (2015) 1530011
1. Introduction and History II-173
2. Basic Properties for Lens Equation II-176
2.1. Derivation of the cosmological lens equation II-176
xxvi Contents
2.2. Properties of lens mapping II-179
2.3. Caustic and critical curves II-183
2.3.1. Circular lenses II-184
2.3.2. The Einstein radius and radial arcs II-187
2.3.3. Non-circular lenses II-189
3. Strong Lensing II-190
3.1. Methods of solving the lens equation:
LTM and non-LTM II-190
3.2. Image magnification II-191
3.3. Time delays II-191
3.4. Comparison of lens model software II-194
3.4.1. Non-light traces mass software II-194
3.4.2. Light traces mass software II-194
3.5. Lens statistics II-195
4. Weak Lensing II-196
4.1. Basic method II-197
4.1.1. Shape measurements II-199
4.2. E/B decomposition II-203
4.3. Magnification bias II-206
4.3.1. Simulation test II-206
4.3.2. Higher-order weak lensing-flexion
and HOLICs II-207
4.4. Cluster mass reconstruction II-208
4.4.1. Density profile II-211
4.4.2. Dark matter subhalos in the coma
cluster II-212
4.5. Cosmic shear II-214
4.5.1. How to measure the cosmic density field II-217
5. Conclusion and Future II-219
18. Inflationary cosmology: First 30+ years II-225
Katsuhiko Sato and Jun’ichi Yokoyama
IJMPD 24 (2015) 1530025
1. Introduction II-225
1.1. Developments in Japan II-227
1.2. Developments in Russia II-228
1.3. Inflation paradigm II-230
2. Resolution of Fundamental Problems II-231
3. Realization of Inflation II-233
Contents xxvii
3.1. Three mechanisms II-233
3.2. Inflation scenario II-234
4. Slow-Roll Inflation Models II-236
4.1. Large-field models II-236
4.2. Small-field model II-237
4.3. Hybrid inflation II-238
5. Reheating II-239
6. Generation of Quantum Fluctuations that
Eventually Behave Classically II-242
7. Cosmological Perturbation II-244
8. Generation of Curvature Fluctuations in
Inflationary Cosmology II-246
9. Tensor Perturbation II-249
10. The Most General Single-Field Inflation II-250
10.1. Homogeneous background equations II-251
10.2. Kinetically driven G-inflation II-253
10.3. Potential-driven slow-roll G-inflation II-254
11. Power Spectrum of Perturbations in Generalized
G-inflation II-255
11.1. Tensor perturbations II-255
11.2. Scalar perturbations II-258
12. Inflationary Cosmology and Observations II-261
12.1. Large-field models II-264
12.2. Small-field model II-265
12.3. Hybrid inflation model II-266
12.4. Noncanonical models and multi-field models II-266
13. Conclusion II-267
19. Inflation, string theory and cosmic strings II-273
David F. Chernoff and S.-H. Henry Tye
IJMPD 24 (2015) 1530010
1. Introduction II-273
2. The Inflationary Universe II-277
3. String Theory and Inflation II-280
3.1. String theory and flux compactification II-281
3.2. Inflation in string theory II-282
4. Small r Scenarios II-283
4.1. Brane inflation II-284
4.1.1. D3-¯D3-brane inflation II-285
xxviii Contents
4.1.2. Inflection point inflation II-286
4.1.3. DBI model II-286
4.1.4. D3-D7-brane inflation II-287
4.2. K¨ahler moduli inflation II-287
5. Large r Scenarios II-288
5.1. The Kim–Nilles–Peloso mechanism II-288
5.1.1. Natural inflation II-288
5.1.2. N-flation II-288
5.1.3. Helical inflation II-290
5.2. Axion monodromy II-291
5.3. Discussions II-292
6. Relics: Low Tension Cosmic Strings II-293
6.1. Strings in brane world cosmology II-296
6.2. Current bounds on string tension Gμ and
probability of intercommutation p II-297
7. Scaling, Slowing, Clustering and Evaporating II-299
7.1. Large-scale string distribution II-302
7.2. Local string distribution II-305
8. Detection II-307
8.1. Detection via Microlensing II-307
8.2. WFIRST microlensing rates II-307
8.3. Gravitational waves II-311
9. Summary II-314
Part V. Quantum Gravity II-323
20. Quantum gravity: A brief history of ideas
and some outlooks II-325
Steven Carlip, Dah-Wei Chiou, Wei-Tou Ni
and Richard Woodard
IJMPD 24 (2015) 1530028
1. Prelude II-325
2. Perturbative Quantum Gravity II-327
3. String Theory II-328
4. Loop Quantum Gravity II-332
5. Black Hole Thermodynamics II-334
6. Quantum Gravity Phenomenology II-337
21. Perturbative quantum gravity comes of age II-349
R. P. Woodard
IJMPD 23 (2014) 1430020
Contents xxix
1. Introduction II-349
2. Why Quantum Gravitational Effects from
Primordial Inflation are Observable II-351
2.1. The background geometry II-351
2.2. Inflationary particle production II-355
3. Tree Order Power Spectra II-358
3.1. The background for single-scalar inflation II-359
3.2. Gauge-fixed, constrained action II-360
3.3. Tree order power spectra II-363
3.4. The controversy over adiabatic regularization II-369
3.5. Why these are quantum gravitational effects II-369
4. Loop Corrections to the Power Spectra II-371
4.1. How to make computations II-372
4.2. -Suppression and late-time growth II-376
4.3. Nonlinear extensions II-380
4.4. The promise of 21 cm radiation II-382
5. Other Quantum Gravitational Effects II-384
5.1. Linearized effective field equations II-384
5.2. Propagators and tensor 1PI functions II-386
5.3. Results and open problems II-395
5.4. Back-Reaction II-399
6. Conclusions II-402
22. Black hole thermodynamics II-415
S. Carlip
IJMPD 23 (2014) 1430023
1. Introduction II-415
2. Prehistory: Black Hole Mechanics and Wheeler’s
Cup of Tea II-416
3. Hawking Radiation II-418
3.1. Quantum field theory in curved spacetime II-419
3.2. Hawking’s calculation II-420
4. Back-of-the-Envelope Estimates II-422
4.1. Entropy II-422
4.2. Temperature II-423
5. The Many Derivations of Black Hole
Thermodynamics II-424
5.1. Other settings II-425
5.2. Unruh radiation II-425
xxx Contents
5.3. Particle detectors II-426
5.4. Tunneling II-426
5.5. Hawking radiation from anomalies II-427
5.6. Periodic Greens functions II-428
5.7. Periodic Gravitational partition function II-429
5.8. Periodic Pair production of black holes II-431
5.9. Periodic Quantum field theory and the
eternal black hole II-431
5.10. Periodic Quantized gravity and classical
matter II-432
5.11. Periodic Other approaches II-433
6. Thermodynamic Properties of Black Holes II-433
6.1. Periodic Black hole evaporation II-434
6.2. Periodic Heat capacity II-434
6.3. Periodic Phase transitions II-435
6.4. Periodic Thermodynamic volume II-435
6.5. Periodic Lorentz violation and perpetual
motion machines II-436
7. Approaches to Black Hole Statistical Mechanics II-437
7.1. Periodic “Phenomenology” II-437
7.2. Periodic Entanglement entropy II-438
7.3. Periodic String theory II-440
7.3.1. Weakly coupled strings and branes II-440
7.3.2. Fuzzballs II-441
7.3.3. The AdS/CFT correspondence II-441
7.4. Loop quantum gravity II-442
7.4.1. Microcanonical approach II-442
7.4.2. Microcanonical approach II-444
7.5. Other ensembles II-445
7.6. Induced gravity II-445
7.7. Logarithmic corrections II-446
8. The Holographic Conjecture II-446
9. The Problem of Universality II-448
9.1. State-counting in conformal field theory II-449
9.2. Application to black holes II-450
9.3. Effective descriptions II-451
10. The Information Loss Problem II-451
10.1. Nonunitary evolution II-452
Contents xxxi
10.2. No black holes II-452
10.3. Remnants and baby universes II-453
10.4. Hawking radiation as a pure state II-454
11. Conclusion II-455
Appendix A. Classical Black Holes II-456
23. Loop quantum gravity II-467
Dah-Wei Chiou
IJMPD 24 (2015) 1530005
1. Introduction II-467
2. Motivations II-469
2.1. Why quantum gravity? II-469
2.2. Difficulties of quantum gravity II-470
2.3. Background-independent approach II-470
3. Connection Theories of General Relativity II-471
3.1. Connection dynamics II-471
3.2. Canonical (Hamiltonian) formulation II-473
3.3. Remarks on connection theories II-476
4. Quantum Kinematics II-478
4.1. Quantization scheme II-478
4.2. Cylindrical functions II-479
4.3. Spin networks II-481
4.4. S-knots II-483
5. Operators and Quantum Geometry II-486
5.1. Holonomy operator II-486
5.2. Area operator II-487
5.3. Volume operator II-489
5.4. Quantum geometry II-490
6. Scalar Constraint and Quantum Dynamics II-492
6.1. Regulated classical scalar constraint II-492
6.2. Quantum scalar constraint II-495
6.3. Solutions to the scalar constraint II-498
6.4. Quantum dynamics II-500
7. Inclusion of Matter Fields II-503
7.1. Yang–Mills fields II-503
7.2. Fermions II-504
7.3. Scalar fields II-505
7.4. S-knots of geometry and matter II-506
xxxii Contents
8. Low-Energy Physics II-507
8.1. Weave states II-507
8.2. Loop states versus Fock states II-508
8.3. Holomorphic coherent states II-508
9. Spin Foam Theory II-511
9.1. From s-knots to spin foams II-511
9.2. Spin foam formalism II-514
10. Black Hole Thermodynamics II-515
10.1. Statistical ensemble II-516
10.2. Bekenstein–Hawking entropy II-517
10.3. More on black hole entropy II-519
11. Loop Quantum Cosmology II-520
11.1. Symmetry reduction II-520
11.2. Quantum kinematics II-522
11.3. Quantum constraint operator II-524
11.4. Physical Hilbert space II-526
11.5. Quantum dynamics II-527
11.6. Other models II-528
12. Current Directions and Open Issues II-529
12.1. The master constraint program II-529
12.2. Algebraic quantum gravity II-530
12.3. Reduced phase space quantization II-530
12.4. Off-shell closure of quantum constraints II-532
12.5. Loop quantum gravity versus spin foam theory II-533
12.6. Covariant loop quantum gravity II-533
12.7. Spin foam cosmology II-534
12.8. Quantum reduced loop gravity II-534
12.9. Cosmological perturbations in the Planck era II-534
12.10. Spherically symmetric loop gravity II-535
12.11. Planck stars and black hole fireworks II-535
12.12. Information loss problem II-536
12.13. Quantum gravity phenomenology II-537
12.14. Supersymmetry and other dimensions II-537
Subject Index I
Author Index XIII