BINARY BLACK HOLE MERGERS AND NOVEL APPROACHES TO GRAVITATIONAL WAVE EXTRACTION IN NUMERICAL RELATIVITY

By C. DAIRO

CONTENTS I FOUNDATIONS AND MATHEMATICAL THEORY VACUUM BINARY BLACK HOLE SPACETIMES THE EINSTEIN EQUATIONS BLACK HOLES ASYMPTOTICS GRAVITATIONAL WAVES BINARY BLACK HOLE SYSTEMS THE THREE STAGES OF BINARY BLACK HOLE COALESCENCE; PARAMETER SPACE AND PROPERTIES OF THE REMNANT; THE CAUCHY EVOLUTION SYSTEM THE ADM FORMALISM THE BSSNOK FORMULATION CHOOSING THE RIGHT GAUGE INITIAL DATA DEALING WITH SPACETIME SINGULARITIES PUNCTURE EVOLUTION; THE CHARACTERISTIC EVOLUTION SYSTEM THE BONDI-SACHS METRIC THE EINSTEIN EQUATIONS IN A CHARACTERISTIC FORMULATION FORMULATION IN TERMS OF SPIN-WEIGHTED SCALARS; ANGULAR COORDINATE BASIS; RADIAL COMPACTI?CATION; THE EVOLUTION SYSTEM; THE CONSTRAINT EQUATIONS; HORIZONS EVENT HORIZONS APPARENT HORIZONS ISOLATED AND DYNAMICAL HORIZONS ISOLATED HORIZONS; DYNAMICAL HORIZONS; MASS AND SPIN; GRAVITATIONAL WAVE EXTRACTION: THEORY EXTRACTION I: COMPLEX WEYL SCALARS EXTRACTION II: GAUGE-INVARIANT PERTURBATIONS OF SCHWARZSCHILD EXTRACTION III: CAUCHY-CHARACTERISTIC EXTRACTION THE GRAVITATIONAL-WAVE STRAIN RADIATED ENERGY RADIATED LINEAR MOMENTUM RADIATED ANGULAR MOMENTUM THE RADIATED ANGULAR MOMENTUM FROM THE WEYL COMPONENT ?4; THE RADIATED ANGULAR MOMENTUM FROM GAUGE-INVARIANT MASTER-FUNCTIONS; II NUMERICS AND IMPLEMENTATION DISCRETIZATION OF HYPERBOLIC PDES FINITE DI?ERENCES METHOD OF LINES STABILITY AND WELL-POSEDNESS HYPERBOLICITY CONVERGENCE AND CONSISTENCY CONTENTS TESTING FOR CONVERGENCE; COMPUTATIONAL INFRASTRUCTURE THE CACTUS COMPUTATIONAL TOOLKIT ADAPTIVE MESH RE?NEMENT MULTIBLOCK SCHEMES SPHERICAL SLICES VARIABLE REGISTRATION; PARALLELIZATION; INTERFACE; SURFACE INTEGRATION; HARMONIC DECOMPOSITION; DISCRETIZATION OF THE EVOLUTION SYSTEMS THE CAUCHY SYSTEM THE CHARACTERISTIC SYSTEM STRUCTURE OF THE NUMERICAL GRID; NUMERICAL IMPLEMENTATION OF THE QUASI-SPHERICAL APPROXIMATION; THE FULL NON-LINEAR DISCRETIZATION; GRAVITATIONAL WAVE EXTRACTION: IMPLEMENTATION CAUCHY CHARACTERISTIC EXTRACTION PSICLOPS WAVEEXTRACT PSI4LAB 10 VISUALIZATION OF SIMULATION DATA 10 1 A VISIT DATABASE PLUGIN FOR CARPET AMR AND CURVI-LINEAR MESHES CONSTRUCTION OF METADATA; CONSTRUCTION OF MESHES; READING OF DATA; EXAMPLES; III SIMULATIONS AND PHYSICS 11 BINARY BLACK HOLE MERGER SIMULATIONS 11 1 SPIN-ALIGNED BINARIES SPIN-KICK CON?GURATIONS; CON?GURATIONS WITH LARGER INITIAL SEPARATION; CONTENTS EQUAL-MASS NON-SPINNING REFERENCE CON?GURATION; 11 2 CONVERGENCE AND ACCURACY TESTS CONVERGENCE OF THE CCATIE CODE; CONVERGENCE AND ACCURACY OF THE LLAMA CODE; CONVERGENCE OF THE CHARACTERISTIC CODE; CONSERVATION OF MASS AND ANGULAR MOMENTUM; A COMPARISON OF WAVE-EXTRACTION METHODS AND TEST FOR PEELING; THE IN?UENCE OF UPWINDED ADVECTION STENCILS; HIGH ORDER ?NITE DI?ERENCING; CHOICE OF CONFORMAL VARIABLE; 11 3 RING-DOWN AND QUASI-NORMAL MODES 11 4 COMPARING DI?ERENT SIMULATION CODES 12 GRAVITATIONAL RECOIL OF BINARY BLACK HOLE MERGERS 12 1 SYSTEMATIC STUDIES ON A RESTRICTED SET OF SPIN-ALIGNED BINARIES INITIAL TRANSIENTS IN THE WAVEFORMS; RECOIL VELOCITIES; MODE CONTRIBUTIONS TO THE RECOIL VELOCITY; ON THE IN?UENCE OF ORBITAL ECCENTRICITY; CONCLUSIONS; 12 2 PARAMETER SPACE OF EQUAL-MASS SPIN-ALIGNED BINARIES SPIN DIAGRAMS AND ?TS; 13 FINAL SPIN OF THE MERGER REMNANT 13 1 SPIN OF EQUAL-MASS SPIN-ALIGNED BINARIES FITTING FORMULA; 13 2 EXTENSION TO UNEQUAL-MASS SPIN-ALIGNED BINARIES METHODS AND RESULTS; 13 3 EXTENSION TO GENERIC MASS-RATIOS AND SPINS ASSUMPTIONS; ANALYTIC EXPRESSION; RESULTS; 14 GRAVITATIONAL-WAVE DETECTABILITY OF BLACK-HOLE BINARIES 14 1 INTRODUCTION 14 2 GRAVITATIONAL-WAVE OBSERVABLES NUMERICAL RELATIVITY WAVEFORMS; MATCHING PN AND NR WAVEFORM AMPLITUDES; RADIATED ENERGY; SNR, HORIZON DISTANCES AND EVENT RATES; 14 3 RESULTS HORIZON DISTANCES AND SNRS; IN?UENCE OF HIGHER ?-MODES; MATCH BETWEEN DI?ERENT MODELS; ACCURACY OF NR WAVEFORM AMPLITUDES; 14 4 FITTING FORMULAS SNR; RADIATED ENERGY; 14 5 CONCLUSIONS 15 GRAVITATIONAL WAVE EXTRACTION: RESULTS 15 1 THE ASYMPTOTIC FALL-O?OF LOCAL WAVEFORM MEASUREMENTS TAKING ADVANTAGE OF MULTIBLOCK SCHEMES; EXTRAPOLATION TO IN?NITY; PEELING PROPERTIES; DISCUSSION; 15 2 UNAMBIGUOUS DETERMINATION OF GRAVITATIONAL WAVEFORMS CAUCHY EVOLUTION; CAUCHY CHARACTERISTIC EXTRACTION; TEST WITH A SCHWARZSCHILD BLACK HOLE AND GAUGE INVARIANCE; BINARY BLACK HOLE MERGER WAVEFORM; OBSERVATIONAL SIGNI?CANCE; INVARIANCE WITH RESPECT TO WORLD-TUBE LOCATION; NOTES ON CHARACTERISTIC CODE SETTINGS; CONTENTS 16 SUMMARY AND OUTLOOK