GRAVITATIONAL WAVES
CONTENTS GRAVITATIONAL WAVES, THEORY AND EXPERIMENT (AN OVERVIEW) REFERENCES PART GRAVITATIONAL WAVES, SOURCES AND DETECTORS BERNARD F SCHUTZ AND FRANCO RICCI SYNOPSIS ELEMENTS OF GRAVITATIONAL WAVES MATHEMATICS OF LINEARIZED THEORY USING THE TT GAUGE TO UNDERSTAND GRAVITATIONAL WAVES INTERACTION OF GRAVITATIONAL WAVES WITH DETECTORS ANALYSIS OF BEAM DETECTORS RANGING TO SPACECRAFT PULSAR TIMING INTERFEROMETRY EXERCISES FOR CHAPTER GRAVITATIONAL-WAVE DETECTORS GRAVITATIONAL-WAVE OBSERVABLES THE PHYSICS OF INTERFEROMETERS NEW INTERFEROMETERS AND THEIR CAPABILITIES THE PHYSICS OF RESONANT MASS DETECTORS NEW BAR DETECTORS AND THEIR CAPABILITIES A DETECTOR IN SPACE LISA’S CAPABILITIES GRAVITATIONAL AND ELECTROMAGNETIC WAVES COMPARED AND CONTRASTED ASTROPHYSICS OF GRAVITATIONAL-WAVE SOURCES SOURCES DETECTABLE FROM GROUND AND FROM SPACE SUPERNOVAE AND GRAVITATIONAL COLLAPSE BINARY STARS CHIRPING BINARY SYSTEMS PULSARS AND OTHER SPINNING NEUTRON STARS RANDOM BACKGROUNDS THE UNEXPECTED WAVES AND ENERGY VARIATIONAL PRINCIPLE FOR GENERAL RELATIVITY VARIATIONAL PRINCIPLES AND THE ENERGY IN GRAVITATIONAL WAVES GAUGE TRANSFORMATION AND INVARIANCE GRAVITATIONAL-WAVE ACTION PRACTICAL APPLICATIONS OF THE ISAACSON ENERGY CURVATURE PRODUCED BY WAVES COSMOLOGICAL BACKGROUND OF RADIATION OTHER APPROACHES MASS- AND CURRENT-QUADRUPOLE RADIATION EXPANSION FOR THE FAR ?ELD OF A SLOW-MOTION SOURCE APPLICATION OF THE TT GAUGE TO THE MASS QUADRUPOLE ?ELD THE TT GAUGE TRANSFORMATIONS QUADRUPOLE ?ELD IN THE TT GAUGE RADIATION PATTERNS RELATED TO THE MOTION OF SOURCES APPLICATION OF THE TT GAUGE TO THE CURRENT-QUADRUPOLE ?ELD THE ?ELD AT THIRD ORDER IN SLOW-MOTION SEPARATING THE CURRENT QUADRUPOLE FROM THE MASS OCTUPOLE A MODEL SYSTEM RADIATING CURRENT-QUADRUPOLE RADIATION ENERGY RADIATED IN GRAVITATIONAL WAVES MASS-QUADRUPOLE RADIATION CURRENT-QUADRUPOLE RADIATION RADIATION IN THE NEWTONIAN LIMIT SOURCE CALCULATIONS RADIATION FROM A BINARY SYSTEM CORRECTIONS THE R-MODES LINEAR GROWTH OF THE R-MODES NONLINEAR EVOLUTION OF THE STAR DETECTION OF R-MODE RADIATION CONCLUSION SOLUTIONS TO EXERCISES GRAVITATIONAL-WAVE DETECTORS GUIDO PIZZELLA, ANGELA DI VIRGILIO, PETER BENDER AND FRANCESCO FUCITO RESONANT DETECTORS FOR GRAVITATIONAL WAVES AND THEIR BANDWIDTH SENSITIVITY AND BANDWIDTH OF RESONANT DETECTORS SENSITIVITY FOR VARIOUS GW SIGNALS RECENT RESULTS OBTAINED WITH THE RESONANT DETECTORS DISCUSSION AND CONCLUSIONS THE EARTH-BASED LARGE INTERFEROMETER VIRGO AND THE LOW FREQUENCY FACILITY INTRODUCTION INTERFEROMETER PRINCIPLES AND VIRGO PARAMETERS THE SA SUSPENSION AND REQUIREMENTS ON THE CONTROL A FEW WORDS ABOUT THE LOW FREQUENCY FACILITY 10 LISA: A PROPOSED JOINT ESA–NASA GRAVITATIONAL-WAVE MISSION 101 DESCRIPTION OF THE LISA MISSION 1011 INTRODUCTION 1012 OVERALL ANTENNA AND SPACECRAFT DESIGN 1013 OPTICS AND INTERFEROMETRY SYSTEM 1014 FREE MASS SENSORS 1015 MICRONEWTON THRUSTERS 1016 MISSION SCENARIO 102 EXPECTED GRAVITATIONAL-WAVE RESULTS FROM LISA 1021 LISA SENSITIVITY AND GALACTIC SOURCES 1022 ORIGIN OF MASSIVE BLACK HOLES 1023 MASSIVE BLACK HOLES IN NORMAL GALAXIES 1024 STRUCTURE FORMATION AND MASSIVE BLACK HOLE COALESCENCE 1025 FUNDAMENTAL PHYSICS TESTS WITH LISA 1026 FUTURE PROSPECTS ACKNOWLEDGMENTS 11 DETECTION OF SCALAR GRAVITATIONAL WAVES 111 INTRODUCTION 112 TESTING THEORIES OF GRAVITY 1121 FREE VIBRATIONS OF AN ELASTIC SPHERE 1122 INTERACTION OF A METRIC GW WITH THE SPHERE VIBRATIONAL MODES 1123 MEASUREMENTS OF THE SPHERE VIBRATIONS AND WAVE POLARIZATION STATES 113 GRAVITATIONAL WAVE RADIATION IN THE JBD THEORY 1131 SCALAR AND TENSOR GWS IN THE JBD THEORY 1132 POWER EMITTED IN GWS 1133 POWER EMITTED IN SCALAR GWS 1134 SCALAR GWS 1135 DETECTABILITY OF THE SCALAR GWS 114 THE HOLLOW SPHERE 115 SCALAR–TENSOR CROSS SECTIONS THE STOCHASTIC GRAVITATIONAL-WAVE BACKGROUND D BABUSCI, S FOFFA, G LOSURDO, M MAGGIORE, G MATONE AND R STURANI 12 GENERALITIES ON THE STOCHASTIC GW BACKGROUND 121 INTRODUCTION 122 DE?NITIONS 1221 GW( F ) AND THE OPTIMAL SNR 1222 THE CHARACTERISTIC AMPLITUDE 1223 THE CHARACTERISTIC NOISE LEVEL 123 THE OVERLAP REDUCTION FUNCTION 1231 TWO INTERFEROMETERS 1232 INTERFEROMETER—BAR 1233 INTERFEROMETER—SPHERE 124 ACHIEVABLE SENSITIVITIES TO THE SGWB 1241 SINGLE DETECTORS 1242 TWO DETECTORS 1243 MORE THAN TWO DETECTORS 125 OBSERVATIONAL BOUNDS 13 SOURCES OF SGWB 131 TOPOLOGICAL DEFECTS 1311 STRINGS 1312 HYBRID DEFECTS 132 IN?ATION 1321 CLASSICAL PICTURE 1322 CALCULATION OF THE SPECTRUM 133 STRING COSMOLOGY 1331 THE MODEL 1332 OBSERVATIONAL BOUNDS TO THE SPECTRUM 134 FIRST-ORDER PHASE TRANSITIONS 135 ASTROPHYSICAL SOURCES THEORETICAL DEVELOPMENTS HERMANN NICOLAI, ALESSANDRO NAGAR, DONATO BINI, FERNANDO DE FELICE, MAURIZIO GASPERINI AND LUC BLANCHET 14 IN?NITE-DIMENSIONAL SYMMETRIES IN GRAVITY 141 EINSTEIN THEORY 1411 INTRODUCTION 1412 MATHEMATICAL CONVENTIONS 1413 THE EINSTEIN–HILBERT ACTION 1414 DIMENSIONAL REDUCTION D = 4 ?D = 1415 DIMENSIONAL REDUCTION D = 3 ?D = 142 NONLINEAR ?-MODELS 1421 EHLERS LAGRANGIAN AS A NONLINEAR ?-MODEL 1422 THE ERNST EQUATION 1423 THE MATZNER–MISNER LAGRANGIAN AS A NONLINEAR ?-MODEL 143 SYMMETRIES OF NONLINEAR ?-MODELS 1431 NONLINEAR REALIZATION OF SL(2, RR)E 1432 NONLINEAR REALIZATION OF SL(2, RR)MM 144 THE GEROCH GROUP 1442 ACTION OF SL(2, RR)MM ON ?, B 1443 THE AF?NE KAC–MOODY SL(2, RR) ALGEBRA 145 THE LINEAR SYSTEM 1451 SOLVING EINSTEIN’S EQUATIONS 1452 THE LINEAR SYSTEM 1453 DERIVATION OF THE COLLIDING PLANE METRIC BY FACTORIZATION FURTHER READING 15 GYROSCOPES AND GRAVITATIONAL WAVES 151 INTRODUCTION 152 SPLITTING FORMALISM AND TEST PARTICLE MOTION: A SHORT REVIEW 153 THE SPACETIME METRIC 154 SEARCHING FOR AN OPERATIONAL FRAME 155 PRECESSION OF A GYROSCOPE IN GEODESIC MOTION 156 CONCLUSIONS 16 ELEMENTARY INTRODUCTION TO PRE-BIG BANG COSMOLOGY AND TO THE RELIC GRAVITON BACKGROUND 161 INTRODUCTION 162 MOTIVATIONS: DUALITY SYMMETRY 163 KINEMATICS: SHRINKING HORIZONS 164 OPEN PROBLEMS AND PHENOMENOLOGICAL CONSEQUENCES 165 COSMOLOGICAL PERTURBATION THEORY 1651 CHOICE OF THE FRAME 1652 CHOICE OF THE GAUGE 1653 NORMALIZATION OF THE AMPLITUDE 1654 COMPUTATION OF THE SPECTRUM 166 THE RELIC GRAVITON BACKGROUND 167 CONCLUSION APPENDIX A THE STRING EFFECTIVE ACTION APPENDIX B DUALITY SYMMETRY APPENDIX C THE STRING COSMOLOGY EQUATIONS 17 POST-NEWTONIAN COMPUTATION OF BINARY INSPIRAL WAVEFORMS 171 INTRODUCTION 172 SUMMARY OF OPTIMAL SIGNAL ?LTERING 173 NEWTONIAN BINARY POLARIZATION WAVEFORMS 174 NEWTONIAN ORBITAL PHASE EVOLUTION 175 POST-NEWTONIAN WAVE GENERATION 1751 FIELD EQUATIONS 1752 SOURCE MOMENTS 1753 RADIATIVE MOMENTS 176 INSPIRAL BINARY WAVEFORM NUMERICAL RELATIVITY EDWARD SEIDEL 18 NUMERICAL RELATIVITY 181 OVERVIEW 182 EINSTEIN EQUATIONS FOR RELATIVITY 1821 CONSTRAINT EQUATIONS 1822 EVOLUTION EQUATIONS 183 STILL NEWER FORMULATIONS: TOWARDS A STABLE EVOLUTION SYSTEM 1831 GENERAL RELATIVISTIC HYDRODYNAMICS 1832 BOUNDARY CONDITIONS 1833 SPECIAL DIF?CULTIES WITH BLACK HOLES 184 TOOLS FOR ANALYSING THE NUMERICAL SPACETIMES 1841 HORIZON ?NDERS 1842 LOCATING THE APPARENT HORIZONS 1843 LOCATING THE EVENT HORIZONS 1844 WAVE EXTRACTION 185 COMPUTATIONAL SCIENCE, NUMERICAL RELATIVITY, AND THE ‘CACTUS’ CODE 1851 THE COMPUTATIONAL CHALLENGES OF NUMERICAL RELATIVITY 186 CACTUS COMPUTATIONAL TOOLKIT 1861 ADAPTIVE MESH RE?NEMENT 187 RECENT APPLICATIONS AND PROGRESS 1871 EVOLVING PURE GRAVITATIONAL WAVES 1872 BLACK HOLES 188 SUMMARY 189 FURTHER READING 1891 OVERVIEWS/FORMALISMS OF NUMERICAL RELATIVITY 1892 NUMERICAL TECHNIQUES 1893 GAUGE CONDITIONS 1894 BLACK HOLE INITIAL DATA 1895 BLACK HOLE EVOLUTION 1896 BLACK HOLE EXCISION 1897 PERTURBATION THEORY AND WAVEFORM EXTRACTION 1898 EVENT AND APPARENT HORIZONS 1899 PURE GRAVITATIONAL WAVES 18910 NUMERICAL CODES