NON-LINEAR OSCILLATIONS OF COMPACT STARS AND GRAVITATIONAL WAVES

By ABIGAIL ROBINSON

TABLE OF CONTENTS INTRODUCTION NON-LINEAR RELATIVISTIC PERTURBATION THEORY MULTI-PARAMETER PERTURBATION THEORY TAYLOR EXPANSION PERTURBATIONS GAUGE TRANSFORMATIONS GAUGE INVARIANT PERTURBATIVE FORMALISM (GSGM) THE TIME DEPENDENT BACKGROUND PERTURBATIVE EQUATIONS NON-LINEAR PERTURBATIVE FRAMEWORK TIME AND FREQUENCY DOMAIN ANALYSIS LINEAR PERTURBATIONS OF COMPACT STARS BACKGROUND GSGM BACKGROUND QUANTITIES FOR LINEAR PERTURBATIONS RADIAL PERTURBATIONS RADIAL PERTURBATIVE EQUATIONS BOUNDARY CONDITIONS FOR RADIAL PERTURBATIONS FREQUENCY DOMAIN ANALYSIS OF RADIAL PERTURBATIONS POLAR NON-RADIAL PERTURBATIONS AXIAL NON-RADIAL PERTURBATIONS NON-LINEAR OSCILLATIONS OF COMPACT STARS COUPLING BETWEEN RADIAL AND NON-RADIAL STELLAR OSCILLATIONS GSGM FORMALISM ON A RADIALLY OSCILLATING STAR COUPLING OF RADIAL AND POLAR NON-RADIAL PERTURBATIONS PERTURBATIVE EQUATIONS FOR POLAR PERTURBATIONS BOUNDARY CONDITIONS FOR POLAR PERTURBATIONS COUPLING OF RADIAL AND AXIAL NON-RADIAL PERTURBATIONS BOUNDARY CONDITIONS FOR AXIAL PERTURBATIONS GAUGE INVARIANCE OF NON-LINEAR PERTURBATIONS CONSTRUCTION OF GAUGE-INVARIANT NON-LINEAR PERTURBATIONS AXIAL PERTURBATIONS POLAR PERTURBATIONS NUMERICAL SIMULATIONS NUMERICAL FRAMEWORK NUMERICAL GRIDS CHARACTERISTIC CURVES AND COURANT-FRIEDRICHS-LEVY CONDITION LINEAR RADIAL PULSATIONS NUMERICAL ALGORITHM BOUNDARY CONDITIONS INITIAL CON?GURATION FOR RADIAL PULSATIONS SIMULATIONS OF RADIAL PERTURBATIONS LINEAR, AXIAL NON-RADIAL OSCILLATIONS BOUNDARY CONDITIONS AND INITIAL CON?GURATION SIMULATIONS FOR AXIAL NON-RADIAL PERTURBATIONS NON-LINEAR AXIAL OSCILLATIONS NUMERICAL ALGORITHMS BOUNDARY AND INITIAL CONDITIONS COUPLING BETWEEN RADIAL PULSATIONS AND AXIAL DIFFERENTIAL ROTATION EFFECTS OF RADIAL PULSATIONS ON THE SCATTERING OF A GRAVITATIONAL WAVE CONCLUSIONS