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- Herausgeber: Wiley-VCH
- Kategorie: Lebensstil
- Sprache: Englisch
- Veröffentlichungsjahr: 2012
This most up-to-date, one-stop reference combines coverage of both theory and observational techniques, with introductory sections to bring all readers up to the same level. Written by outstanding researchers directly involved with the scientific program of the Laser Interferometer Gravitational-Wave Observatory (LIGO), the book begins with a brief review of general relativity before going on to describe the physics of gravitational waves and the astrophysical sources of gravitational radiation. Further sections cover gravitational wave detectors, data analysis, and the outlook of gravitational wave astronomy and astrophysics.
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Contents
Cover
Half Title page
Title page
Copyright page
Dedication
Preface
List of Examples
Introduction
Conventions
References
Chapter 1: Prologue
1.1 Tides in Newton’s Gravity
1.2 Relativity
Chapter 2: A Brief Review of General Relativity
2.1 Differential Geometry
2.2 Slow Motion in Weak Gravitational Fields
2.3 Stress-Energy Tensor
2.4 Einstein’s Field Equations
2.5 Newtonian Limit of General Relativity
2.6 Problems
References
Chapter 3: Gravitational Waves
3.1 Description of Gravitational Waves
3.2 Physical Properties of Gravitational Waves
3.3 Production of Gravitational Radiation
3.4 Demonstration: Rotating Triaxial Ellipsoid
3.5 Demonstration: Orbiting Binary System
3.6 Problems
References
Chapter 4: Beyond the Newtonian Limit
4.1 Post-Newtonian
4.2 Perturbation about Curved Backgrounds
4.3 Numerical Relativity
4.4 Problems
References
Chapter 5: Sources of Gravitational Radiation
5.1 Sources of Continuous Gravitational Waves
5.2 Sources of Gravitational-Wave Bursts
5.3 Sources of a Stochastic Gravitational-Wave Background
5.4 Problems
References
Chapter 6: Gravitational-Wave Detectors
6.1 Ground-Based Laser Interferometer Detectors
6.2 Space-Based Detectors
6.3 Pulsar Timing Experiments
6.4 Resonant Mass Detectors
6.5 Problems
References
Chapter 7: Gravitational-Wave Data Analysis
7.1 Random Processes
7.2 Optimal Detection Statistic
7.3 Parameter Estimation
7.4 Detection Statistics for Poorly Modelled Signals
7.5 Detection in Non-Gaussian Noise
7.6 Networks of Gravitational-Wave Detectors
7.7 Data Analysis Methods for Continuous-Wave Sources
7.8 Data Analysis Methods for Gravitational-Wave Bursts
7.9 Data Analysis Methods for Stochastic Sources
7.10 Problems
References
Chapter 8: Epilogue: Gravitational-Wave Astronomy and Astrophysics
8.1 Fundamental Physics
8.2 Astrophysics
References
Appendix A: Gravitational-Wave Detector Data
A.1 Gravitational-Wave Detector Site Data
A.2 Idealized Initial LIGO Model
References
Appendix B: Post-Newtonian Binary Inspiral Waveform
B.1 TaylorT1 Orbital Evolution
B.2 TaylorT2 Orbital Evolution
B.3 TaylorT3 Orbital Evolution
B.4 TaylorT4 Orbital Evolution
B.5 TaylorF2 Stationary Phase
References
Index
Jolien D. E. Creighton and Warren G. Anderson
Gravitational-Wave Physics and Astronomy
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The Authors
Dr. Jolien D. E. Creighton University of WisconsinMilwaukee Department of Physics P.O. Box 413 Milwaukee,WI 53201 [email protected]
Dr. Warren G. Anderson University of WisconsinMilwaukee Department of Physics P.O. Box 413 Milwaukee,WI 53201 [email protected]
Cover Post-Newtonian apples created by Teviet Creighton. Hubble ultra-deep field image(NASA, ESA, S. Beckwith STScl and the HUDF Team).
All books published byWiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.
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Bibliographic information published by the Deutsche NationalbibliothekThe Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.d-nb.de..
© 2011WILEY-VCHVerlag GmbH&Co. KGaA, Boschstr. 12, 69469 Weinheim, Germany
All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form by photoprinting, microfilm, or any othermeans nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.
ISBN Print 978-3-527-40886-3
ISBN ePDF 978-3-527-63605-1ISBN oBook 978-3-527-63603-7ISBN ePub 978-3-527-63604-4
JDEC: To my grandmother.
WGA: To my parents, who never asked me to stop asking why, although they did stop answering after a while, and to family, Lynda, Ethan and Jacob, who give me the space I need to continue asking.
Preface
During the writing of this book we often had to escape the office for week-long mini-sabbaticals. We would like to thank the Max-Planck-Institut fr Gravitationsphysik (Albert-Einstein-Institute) in Hannover, Germany, for hosting us for one of these sabbaticals, theWarren G. Anderson Office of GravitationalWave Research in Calgary, Alberta for hosting a second one, the University of Minnesota for hosting a third and the University of Cardiff for our final retreat.
We thank, in no particular order (other than alphabetic), Bruce Allen, Patrick Brady, Teviet Creighton, Stephen Fairhurst, John Friedman, Judy Giannakopoulou, Brennan Hughey, Luca Santamara Lara, Vuk Mandic, Chris Messenger, Evan Ochsner, Larry Price, Jocelyn Read, Richard OShaughnessy, Bangalore Sathyaprakash, Peter Saulson, Xavier Siemens, Amber Stuver, Patrick Sutton, Ruslan Vaulin, Alan Weinstein, Madeline White and Alan Wiseman for a great deal of assistance. This work was supported by the National Science Foundation grants PHY- 0701817, PHY-0600953 and PHY-0970074.
Calgary, June 2011
J.D.E.C.
List of Examples
Example 1.1 Coordinate acceleration in non-inertial frames of reference
Example 1.2 Tidal acceleration
Example 2.1 Transformation to polar coordinates
Example 2.2 Volume element
Example 2.3 How are directional derivatives like vectors?
Example 2.4 Flat-space connection in polar coordinates
Example 2.5 Flat-space connection in polar coordinates (again)
Example 2.6 Equation of continuity
Example 2.7 Vector commutation
Example 2.8 Lie derivative
Example 2.9 Curvature
Example 2.10 Riemann tensor in a locally inertial frame
Example 2.11 Geodesic deviation in the weak-field slow-motion limit
Example 2.12 The Euler equations
Example 2.13 Equations of motion for a point particle
Example 2.14 Harmonic coordinates
Example 3.1 Transformation from TT coordinates to a locally inertial frame
Example 3.2 Wave equation for the Riemann tensor
Example 3.3 Attenuation of gravitational waves
Example 3.4 Degrees of freedom of a plane gravitational wave
Example 3.5 Plus- and cross-polarization tensors
Example 3.6 A resonant mass detector
Example 3.7 Order of magnitude estimates of gravitational-wave amplitude
Example 3.8 Fourier solution for the gravitational wave
Example 3.9 Order ofmagnitude estimates of gravitational-wave luminosity
Example 3.10 Gravitational-wave spectrum
Example 3.11 Cross-section of a resonant mass detector
Example 3.12 Point particle in rotating reference frame
Example 3.13 The Crab pulsar
Example 3.14 Newtonian chirp
Example 3.15 The HulseTaylor binary pulsar
Example 4.1 Effective stress-energy tensor
Example 4.2 Amplification of gravitational waves by inflation
Example 4.3 Black hole ringdown radiation
Example 4.4 Analogy with electromagnetism
Example 4.5 The BSSN formulation
Example 5.1 Blandfords argument
Example 5.2 Rate of binary neutron star coalescences in the Galaxy
Example 5.3 Chandrasekhar mass
Example 6.1 Stokes relations
Example 6.2 Dielectric mirror
Example 6.3 Anti-resonant FabryProt cavity
Example 6.4 Michelson interferometer gravitational-wave detector
Example 6.5 Radio-frequency readout
Example 6.6 Standard quantum limit
Example 6.7 Derivation of the fluctuationdissipation theorem
Example 6.8 Coupled oscillators
Example 7.1 Shot noise
Example 7.2 Unknown amplitude
Example 7.3 Sensitivity of a matched filter gravitational-wave search
Example 7.4 Unknown phase
Example 7.5 Measurement accuracy of signal amplitude and phase
Example 7.6 Systematic error in estimate of signal amplitude
Example 7.7 Frequentist upper limits
Example 7.8 Time-frequency excess-power statistic
Example 7.9 Nullspace of two co-aligned, co-located detectors
Example 7.10 Nullspace of three non-aligned detectors
Example 7.11 Sensitivity of the known-pulsar search
Example 7.12 Horizon distance and range
Example 7.13 Overlap reduction function in the long-wavelength limit
Example 7.14 HellingsDowns curve
Example 7.15 Sensitivity of a stochastic background search
Example A.1 Antenna response beampatterns for interferometer detectors
Introduction
This work is intended both as a textbook for an introductory course on gravitational-wave astronomy and as a basic reference on most aspects in this field of research.
As part of the syllabus of a course on gravitational waves, this book could be used to follow a course on General Relativity (in which case, the first chapter could be greatly abbreviated), or as an introductory graduate course (in which case the first chapter is required reading for what follows). Not all material would be covered in a single semester.
Within the text we include examples that elucidate a particular point described in the main text or give additional detail beyond that covered in the body. At the end of each chapter we provide a short reference section that contains suggested further reading. We have not attempted to provide a complete list of work in the field, as one might have in a review article; rather we provide references to seminal papers, to works of particular pedagogic value, and to review articles that will provide the necessary background for researchers. Each chapter also has a selection of problems.
Please see http://www.lsc-group.phys.uwm.edu/∼jolien for an errata for this book. If you find errors that are not currently noted in the errata, please notify [email protected].
Conventions
We use bold sans-serif letters such as T and u to represent generic tensors and spacetime vectors, and italic bold letters such as v to represent purely spatial vectors. When writing the components of such objects, we use Greek letters for the indices for tensors on spacetime, Tαβ and uα, while we use Latin letters for the indices for spatial vectors or matrices, for example vi and Mij. Spacetime indices normally run over four values, so , while spatial indices normally run over three values, , unless otherwise specified. We employ the Einstein summation convention where there is an implied sum over repeated indices (known as dummy indices), so that . In these examples, the indices α and i are not contracted and are called free indices (that is, these are actually four equations in the first case and three equations in the second case since α can have the values 0, 1, 2, or 3, while i can have the values 1, 2, or 3).
We distinguish between the covariant derivative, , and the three-space gradient operator , which is the operator in Cartesian coordinates. The Laplacian is in Cartesian coordinates, and the flat-space d’Alembertian operator is in Cartesian coordinates.
Our spacetime sign convention is so that flat spacetime in Cartesian coordinates has the line element . The sign conventions of common tensors follow that of Misner et al. (1973) and Wald (1984).
The Fourier transform of some time series x(t) is used to find the frequency series according to
(0.1)
while
(0.2)
is the inverse Fourier transform.
References
Misner, C.W., Thorne, K.S. and Wheeler, J.A. (1973) Gravitation, Freeman, San Francisco.
Wald, R.M. (1984) General Relativity, University of Chicago Press.
