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E-grāmata: Gravitational Waves [Taylor & Francis e-book]

Edited by (University of Insubria, Como, Italy), Edited by (University of Insubria, Como, Italy), Edited by (University of Lecce, Italy University of Lecce, Italy), Edited by
  • Formāts: 412 pages
  • Izdošanas datums: 11-Sep-2019
  • Izdevniecība: CRC Press
  • ISBN-13: 9780429146572
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Gravitational WavesPalielināt
  • Formāts: 412 pages
  • Izdošanas datums: 11-Sep-2019
  • Izdevniecība: CRC Press
  • ISBN-13: 9780429146572
Citas grāmatas par šo tēmu:
Taylor & Francis e-booksMore info about Taylor & Francis e-books
Rokasgrāmatas mājas lapa: https://www.taylorfrancis.com/books/9780429146572
Gravitational waves (GWs) are a hot topic and promise to play a central role in astrophysics, cosmology, and theoretical physics. Technological developments have led us to the brink of their direct observation, which could become a reality in the coming years. The direct observation of GWs will open an entirely new field: GW astronomy. This is expected to bring a revolution in our knowledge of the universe by allowing the observation of previously unseen phenomena, such as the coalescence of compact objects (neutron stars and black holes), the fall of stars into supermassive black holes, stellar core collapses, big-bang relics, and the new and unexpected.

With a wide range of contributions by leading scientists in the field, Gravitational Waves covers topics such as the basics of GWs, various advanced topics, GW detectors, astrophysics of GW sources, numerical applications, and several recent theoretical developments. The material is written at a level suitable for postgraduate students entering the field.
Preface xiii
1 Gravitational waves, theory and experiment (an overview)
1(10)
References
9(2)
PART I Gravitational Waves, Sources and Detectors
11(78)
Bernard F. Schutz
Franco Ricci
Synopsis
13(2)
2 Elements of gravitational waves
15(9)
2.1 Mathematics of linearized theory
16(1)
2.2 Using the TT gauge to understand gravitational waves
17(2)
2.3 Interaction of gravitational waves with detectors
19(2)
2.4 Analysis of beam detectors
21(1)
2.4.1 Ranging to spacecraft
21(1)
2.4.2 Pulsar timing
22(1)
2.4.3 Interferometry
22(1)
2.5 Exercises for chapter 2
22(2)
3 Gravitational-wave detectors
24(19)
3.1 Gravitational-wave observables
26(2)
3.2 The physics of interferometers
28(6)
3.2.1 New interferometers and their capabilities
32(2)
3.3 The physics of resonant mass detectors
34(4)
3.3.1 New bar detectors and their capabilities
37(1)
3.4 A detector in space
38(3)
3.4.1 LISA's capabilities
39(2)
3.5 Gravitational and electromagnetic waves compared and contrasted
41(2)
4 Astrophysics of gravitational-wave sources
43(7)
4.1 Sources detectable from ground and from space
43(7)
4.1.1 Supernovae and gravitational collapse
43(1)
4.1.2 Binary stars
44(1)
4.1.3 Chirping binary systems
44(2)
4.1.4 Pulsars and other spinning neutron stars
46(2)
4.1.5 Random backgrounds
48(1)
4.1.6 The unexpected
49(1)
5 Waves and energy
50(8)
5.1 Variational principle for general relativity
50(1)
5.2 Variational principles and the energy in gravitational waves
51(3)
5.2.1 Gauge transformation and invariance
52(1)
5.2.2 Gravitational-wave action
52(2)
5.3 Practical applications of the Isaacson energy
54(2)
5.3.1 Curvature produced by waves
55(1)
5.3.2 Cosmological background of radiation
55(1)
5.3.3 Other approaches
56(1)
5.4 Exercises for chapter 5
56(2)
6 Mass- and current-quadrupole radiation
58(13)
6.1 Expansion for the far field of a slow-motion source
58(2)
6.2 Application of the TT gauge to the mass quadrupole field
60(4)
6.2.1 The TT gauge transformations
60(1)
6.2.2 Quadrupole field in the TT gauge
61(1)
6.2.3 Radiation patterns related to the motion of sources
62(2)
6.3 Application of the TT gauge to the current-quadrupole field
64(4)
6.3.1 The field at third order in slow-motion
64(1)
6.3.2 Separating the current quadrupole from the mass octupole
65(2)
6.3.3 A model system radiating current-quadrupole radiation
67(1)
6.4 Energy radiated in gravitational waves
68(2)
6.4.1 Mass-quadrupole radiation
69(1)
6.4.2 Current-quadrupole radiation
69(1)
6.5 Radiation in the Newtonian limit
70(1)
7 Source calculations
71(18)
7.1 Radiation from a binary system
71(2)
7.1.1 Corrections
73(1)
7.2 The r-modes
73(7)
7.2.1 Linear growth of the r-modes
76(1)
7.2.2 Nonlinear evolution of the star
77(2)
7.2.3 Detection of r-mode radiation
79(1)
7.3 Conclusion
80(1)
References
81(3)
Solutions to exercises
84(5)
PART 2 Gravitational-wave detectors
89(90)
Guido Pizzella
Angela Di Virgilio
Peter Bender
Francesco Fucito
8 Resonant detectors for gravitational waves and their bandwidth
91(12)
8.1 Sensitivity and bandwidth of resonant detectors
91(4)
8.2 Sensitivity for various GW signals
95(4)
8.3 Recent results obtained with the resonant detectors
99(2)
8.4 Discussion and conclusions
101(1)
References
102(1)
9 The Earth-based large interferometer Virgo and the Low Frequency Facility
103(12)
9.1 Introduction
103(5)
9.1.1 Interferometer principles and Virgo parameters
104(4)
9.2 The SA suspension and requirements on the control
108(3)
9.3 A few words about the Low Frequency Facility
111(1)
9.4 Conclusion
112(2)
References
114(1)
10 LISA: A proposed joint ESA--NASA gravitational-wave mission
115(37)
10.1 Description of the LISA mission
115(17)
10.1.1 Introduction
115(1)
10.1.2 Overall antenna and spacecraft design
116(5)
10.1.3 Optics and interferometry system
121(4)
10.1.4 Free mass sensors
125(4)
10.1.5 Micronewton thrusters
129(2)
10.1.6 Mission scenario
131(1)
10.2 Expected gravitational-wave results from LISA
132(16)
10.2.1 LISA sensitivity and galactic sources
132(4)
10.2.2 Origin of massive black holes
136(2)
10.2.3 Massive black holes in normal galaxies
138(3)
10.2.4 Structure formation and massive black hole coalescence
141(2)
10.2.5 Fundamental physics tests with LISA
143(3)
10.2.6 Future prospects
146(2)
Acknowledgments
148(1)
References
148(4)
11 Detection of scalar gravitational waves
152(27)
11.1 Introduction
152(2)
11.2 Testing theories of gravity
154(5)
11.2.1 Free vibrations of an elastic sphere
154(1)
11.2.2 Interaction of a metric GW with the sphere vibrational modes
155(2)
11.2.3 Measurements of the sphere vibrations and wave polarization states
157(2)
11.3 Gravitational wave radiation in the JBD theory
159(9)
11.3.1 Scalar and Tensor GWs in the JBD Theory
160(1)
11.3.2 Power emitted in GWs
161(1)
11.3.3 Power emitted in scalar GWs
162(2)
11.3.4 Scalar GWs
164(1)
11.3.5 Detectability of the scalar GWs
165(3)
11.4 The hollow sphere
168(2)
11.5 Scalar--tensor cross sections
170(6)
Acknowledgments
176(1)
References
176(3)
PART 3 The Stochastic Gravitational-Wave Background
179(64)
D. Babusci
S. Foffa
G. Losurdo
M. Maggiore
G. Matone
R. Sturani
12 Generalities on the stochastic GW background
181(30)
12.1 Introduction
181(3)
12.2 Definitions
184(7)
12.2.1 Ωgw(ƒ) and the optimal SNR
184(3)
12.2.2 The characteristic amplitude
187(2)
12.2.3 The characteristic noise level
189(2)
12.3 The overlap reduction function
191(6)
12.3.1 Two interferometers
193(3)
12.3.2 Interferometer---bar
196(1)
12.3.3 Interferometer---sphere
196(1)
12.4 Achievable sensitivities to the SGWB
197(10)
12.4.1 Single detectors
197(2)
12.4.2 Two detectors
199(5)
12.4.3 More than two detectors
204(3)
12.5 Observational bounds
207(4)
13 Sources of SGWB
211(32)
13.1 Topological defects
211(12)
13.1.1 Strings
214(7)
13.1.2 Hybrid defects
221(2)
13.2 Inflation
223(6)
13.2.1 Classical picture
224(1)
13.2.2 Calculation of the spectrum
225(4)
13.3 String cosmology
229(6)
13.3.1 The model
230(4)
13.3.2 Observational bounds to the spectrum
234(1)
13.4 First-order phase transitions
235(2)
13.5 Astrophysical sources
237(2)
References
239(4)
PART 4 Theoretical developments
243(116)
Hermann Nicolai
Alessandro Nagar
Donato Bini
Fernando De Felice
Maurizio Gasperini
Luc Blanchet
14 Infinite-dimensional symmetries in gravity
245(23)
14.1 Einstein theory
245(7)
14.1.1 Introduction
245(1)
14.1.2 Mathematical conventions
245(2)
14.1.3 The Einstein--Hilbert action
247(1)
14.1.4 Dimensional reduction D = 4 → D = 3
247(1)
14.1.5 Dimensional reduction D = 3 → D = 2
248(4)
14.2 Nonlinear σ-models
252(5)
14.2.1 Ehlers Lagrangian as a nonlinear σ-model
254(1)
14.2.2 The Ernst equation
255(1)
14.2.3 The Matzner--Misner Lagrangian as a nonlinear a-model
255(2)
14.3 Symmetries of nonlinear σ-models
257(2)
14.3.1 Nonlinear realization of SL(2, R)E
257(1)
14.3.2 Nonlinear realization of SL(2, ***R)MM
258(1)
14.4 The Geroch group
259(2)
14.4.1 Action of SL(2, R)E on λ, B2
259(1)
14.4.2 Action of SL(2, R)MM on λ, B
260(1)
14.4.3 The affine Kac--Moody SL(2, R) algebra
260(1)
14.5 The linear system
261(6)
14.5.1 Solving Einstein's equations
261(2)
14.5.2 The linear system
263(2)
14.5.3 Derivation of the colliding plane metric by factorization
265(2)
Acknowledgments
267(1)
Further reading
267(1)
15 Gyroscopes and gravitational waves
268(12)
15.1 Introduction
268(1)
15.2 Splitting formalism and test particle motion: a short review
269(3)
15.3 The spacetime metric
272(2)
15.4 Searching for an operational frame
274(2)
15.5 Precession of a gyroscope in geodesic motion
276(2)
15.6 Conclusions
278(1)
References
278(2)
16 Elementary introduction to pre-big bang cosmology and to the relic graviton background
280(58)
16.1 Introduction
280(3)
16.2 Motivations: duality symmetry
283(6)
16.3 Kinematics: shrinking horizons
289(5)
16.4 Open problems and phenomenological consequences
294(3)
16.5 Cosmological perturbation theory
297(12)
16.5.1 Choice of the frame
297(2)
16.5.2 Choice of the gauge
299(3)
16.5.3 Normalization of the amplitude
302(2)
16.5.4 Computation of the spectrum
304(5)
16.6 The relic graviton background
309(7)
16.7 Conclusion
316(1)
Acknowledgments
316(1)
Appendix A The string effective action
317(5)
Appendix B Duality symmetry
322(6)
Appendix C The string cosmology equations
328(5)
References
333(5)
17 Post-Newtonian computation of binary inspiral waveforms
338(21)
17.1 Introduction
338(2)
17.2 Summary of optimal signal filtering
340(3)
17.3 Newtonian binary polarization waveforms
343(3)
17.4 Newtonian orbital phase evolution
346(3)
17.5 Post-Newtonian wave generation
349(5)
17.5.1 Field equations
349(1)
17.5.2 Source moments
350(2)
17.5.3 Radiative moments
352(2)
17.6 Inspiral binary waveform
354(2)
References
356(3)
PART 5 Numerical relativity
359(50)
Edward Seidel
18 Numerical relativity
361(48)
18.1 Overview
361(2)
18.2 Einstein equations for relativity
363(6)
18.2.1 Constraint equations
365(2)
18.2.2 Evolution equations
367(2)
18.3 Still newer formulations: towards a stable evolution system
369(13)
18.3.1 General relativistic hydrodynamics
376(2)
18.3.2 Boundary conditions
378(1)
18.3.3 Special difficulties with black holes
379(3)
18.4 Tools for analysing the numerical spacetimes
382(6)
18.4.1 Horizon finders
382(1)
18.4.2 Locating the apparent horizons
383(2)
18.4.3 Locating the event horizons
385(1)
18.4.4 Wave extraction
386(2)
18.5 Computational science, numerical relativity, and the `Cactus' code
388(1)
18.5.1 The computational challenges of numerical relativity
388(1)
18.6 Cactus computational toolkit
389(3)
18.6.1 Adaptive mesh refinement
391(1)
18.7 Recent applications and progress
392(7)
18.7.1 Evolving pure gravitational waves
392(2)
18.7.2 Black holes
394(5)
18.8 Summary
399(1)
Acknowledgments
400(1)
18.9 Further reading
400(3)
18.9.1 Overviews/formalisms of numerical relativity
400(1)
18.9.2 Numerical techniques
401(1)
18.9.3 Gauge conditions
401(1)
18.9.4 Black hole initial data
401(1)
18.9.5 Black hole evolution
401(1)
18.9.6 Black hole excision
402(1)
18.9.7 Perturbation theory and waveform extraction
402(1)
18.9.8 Event and apparent horizons
402(1)
18.9.9 Pure gravitational waves
403(1)
18.9.10 Numerical codes
403(1)
References
403(6)
Index 409
I. Ciufolini, V. Gorini, U. Moschella, P Fre
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