THE PROJECT PHYSICS COURSE: TEXT AND HANDBOOK

By JESSICA HERNANDEZ

CONTENTS THE GENERAL RELATIVISTIC TWO-BODY PROBLEM | INTRODUCTION | MULTICHART APPROACH TO THE ??-BODY PROBLEM | EOB DESCRIPTION OF THE CONSERVATIVE DYNAMICS OF TWO-BODY SYSTEMS | EOB DESCRIPTION OF RADIATION REACTION AND OF THE EMITTED WAVEFORM DURING INSPIRAL | EOB DESCRIPTION OF THE MERGER OF BINARY BLACK HOLES AND OF THE RINGDOWN OF THE FINAL BLACK HOLE | EOB VS NR | EOB[NR] WAVEFORMS VS NR ONES | EOB[3PN] DYNAMICS VS NR ONE | OTHER DEVELOPMENTS | EOB WITH SPINNING BODIES | EOB WITH TIDALLY DEFORMED BODIES | EOB AND GSF | CONCLUSIONS | REFERENCES | HAMILTONIAN DYNAMICS OF SPINNING COMPACT BINARIES THROUGH HIGH POST-NEWTONIAN APPROXIMATIONS | HAMILTONIAN FORMULATION OF GENERAL RELATIVITY | POINT PARTICLES | SPINNING PARTICLES | INTRODUCING THE ROUTHIAN | THE POINCARÉ ALGEBRA | POST-NEWTONIAN BINARY HAMILTONIANS | SPINLESS BINARIES | SPINNING BINARIES | BINARY MOTION | SPINLESS TWO-BODY SYSTEMS | PARTICLE MOTION IN KERR GEOMETRY | TWO-BODY SYSTEMS WITH SPINNING COMPONENTS | COVARIANT THEORY OF THE POST-NEWTONIAN EQUATIONS OF MOTION OF EXTENDED BODIES | A THEORY OF GRAVITY FOR POST-NEWTONIAN CELESTIAL MECHANICS | THE FIELD EQUATIONS | THE ENERGY–MOMENTUM TENSOR | PARAMETERIZED POST-NEWTONIAN CELESTIAL MECHANICS | EXTERNAL AND INTERNAL PROBLEMS OF MOTION | SOLVING THE FIELD EQUATIONS BY POST-NEWTONIAN APPROXIMATIONS | THE POST-NEWTONIAN FIELD EQUATIONS | CONFORMAL HARMONIC GAUGE | PARAMETERIZED POST-NEWTONIAN COORDINATES | THE GLOBAL POST-NEWTONIAN COORDINATES | THE LOCAL POST-NEWTONIAN COORDINATES | POST-NEWTONIAN COORDINATE TRANSFORMATIONS BY ASYMPTOTIC MATCHING | GENERAL STRUCTURE OF THE TRANSFORMATION | MATCHING SOLUTION | POST-NEWTONIAN EQUATIONS OF MOTION OF EXTENDED BODIES IN LOCAL COORDINATES | MICROSCOPIC POST-NEWTONIAN EQUATIONS OF MOTION | POST-NEWTONIAN MASS OF AN EXTENDED BODY | POST-NEWTONIAN CENTER OF MASS AND LINEAR MOMENTUM OF AN EXTENDED BODY | TRANSLATIONAL EQUATION OF MOTION IN THE LOCAL COORDINATES | POST-NEWTONIAN EQUATIONS OF MOTION OF EXTENDED BODIES IN GLOBAL COORDINATES | STF EXPANSIONS OF THE EXTERNAL GRAVITATIONAL POTENTIALS IN TERMS OF THE INTERNAL MULTIPOLES | TRANSLATIONAL EQUATIONS OF MOTION | COVARIANT EQUATIONS OF TRANSLATIONAL MOTION OF EXTENDED BODIES | EFFECTIVE BACKGROUND MANIFOLD | GEODESIC MOTION AND 4-FORCE | FOUR-DIMENSIONAL FORM OF MULTIPOLE MOMENTS | COVARIANT TRANSLATIONAL EQUATIONS OF MOTION | COMPARISON WITH DIXON’S TRANSLATIONAL EQUATIONS OF MOTION | ON THE DSX-FRAMEWORK | THE POST-NEWTONIAN FORMALISM | THE GENERAL FORM OF THE METRIC | FIELD EQUATIONS AND THE GAUGE PROBLEM | THE GRAVITATIONAL FIELD OF A BODY | POST-NEWTONIAN MULTIPOLE MOMENTS | GEODESIC MOTION IN THE PN-SCHWARZSCHILD FIELD | ASTRONOMICAL REFERENCE FRAMES | TRANSFORMATION BETWEEN GLOBAL AND LOCAL SYSTEMS: FIRST RESULTS | SPLIT OF LOCAL POTENTIALS, MULTIPOLE MOMENTS | TETRAD INDUCED LOCAL COORDINATES | THE STANDARD TRANSFORMATION BETWEEN GLOBAL AND LOCAL COORDINATES | THE DESCRIPTION OF TIDAL FORCES | THE GRAVITATIONAL ??-BODY PROBLEM | LOCAL EVOLUTION EQUATIONS | THE TRANSLATIONAL MOTION | FURTHER DEVELOPMENTS | GENERAL RELATIVISTIC THEORY OF LIGHT PROPAGATION IN MULTIPOLAR GRAVITATIONAL FIELDS | STATEMENT OF THE PROBLEM | HISTORICAL BACKGROUND | NOTATIONS AND CONVENTIONS | THE METRIC TENSOR, GAUGES AND COORDINATES | THE CANONICAL FORM OF THE METRIC TENSOR PERTURBATION | THE HARMONIC COORDINATES | THE ADM COORDINATES | EQUATIONS OF PROPAGATION OF ELECTROMAGNETIC SIGNALS | MAXWELL EQUATIONS IN CURVED SPACETIME | MAXWELL EQUATIONS IN THE GEOMETRIC OPTICS APPROXIMATION | ELECTROMAGNETIC EIKONAL AND LIGHT-RAY GEODESICS | POLARIZATION OF LIGHT AND THE STOKES PARAMETERS | MATHEMATICAL TECHNIQUE FOR ANALYTIC INTEGRATION OF LIGHT-RAY EQUATIONS | MONOPOLE AND DIPOLE LIGHT-RAY INTEGRALS | LIGHT-RAY INTEGRALS FROM QUADRUPOLE AND HIGHER ORDER MULTIPOLES | GRAVITATIONAL PERTURBATIONS OF THE LIGHT RAY | RELATIVISTIC PERTURBATION OF THE ELECTROMAGNETIC EIKONAL | RELATIVISTIC PERTURBATION OF THE COORDINATE VELOCITY OF LIGHT | PERTURBATION OF THE LIGHT-RAY TRAJECTORY | OBSERVABLE RELATIVISTIC EFFECTS | GRAVITATIONAL TIME DELAY OF LIGHT | GRAVITATIONAL DEFLECTION OF LIGHT | GRAVITATIONAL SHIFT OF FREQUENCY | GRAVITY-INDUCED ROTATION OF THE PLANE OF POLARIZATION OF LIGHT | LIGHT PROPAGATION THROUGH THE FIELD OF GRAVITATIONAL LENS | SMALL PARAMETERS AND ASYMPTOTIC EXPANSIONS | ASYMPTOTIC EXPRESSIONS FOR OBSERVABLE EFFECTS | LIGHT PROPAGATION THROUGH THE FIELD OF PLANE GRAVITATIONAL WAVES | PLANE-WAVE ASYMPTOTIC EXPANSIONS | ON THE BACKREACTION PROBLEM IN COSMOLOGY | FORMULATION AND AVERAGING | CALCULATION IN THE NEWTONIAN GAUGE | DEFINITION OF THE BACKGROUND | POST-NEWTONIAN APPROXIMATIONS IN COSMOLOGY | DERIVATIVES ON THE GEOMETRIC MANIFOLD | VARIATIONAL DERIVATIVE | LIE DERIVATIVE | LAGRANGIAN AND FIELD VARIABLES | ACTION FUNCTIONAL | LAGRANGIAN OF THE IDEAL FLUID | LAGRANGIAN OF SCALAR FIELD | LAGRANGIAN OF A LOCALIZED ASTRONOMICAL SYSTEM | BACKGROUND MANIFOLD | HUBBLE FLOW | FRIEDMANN–LEMÎTRE–ROBERTSON–WALKER METRIC | CHRISTOFFEL SYMBOLS AND COVARIANT DERIVATIVES | RIEMANN TENSOR | THE FRIEDMANN EQUATIONS | HYDRODYNAMIC EQUATIONS OF THE IDEAL FLUID | SCALAR FIELD EQUATIONS | EQUATIONS OF MOTION OF MATTER OF THE LOCALIZED ASTRONOMICAL SYSTEM | LAGRANGIAN PERTURBATIONS OF FLRW MANIFOLD | THE CONCEPT OF PERTURBATIONS | THE PERTURBATIVE EXPANSION OF THE LAGRANGIAN | THE BACKGROUND FIELD EQUATIONS | THE LAGRANGIAN EQUATIONS FOR GRAVITATIONAL FIELD PERTURBATIONS | THE LAGRANGIAN EQUATIONS FOR DARK MATTER PERTURBATIONS | THE LAGRANGIAN EQUATIONS FOR DARK ENERGY PERTURBATIONS | LINEARIZED POST-NEWTONIAN EQUATIONS FOR FIELD VARIABLES | GAUGE-INVARIANT SCALARS AND FIELD EQUATIONS IN 1+3 THREADING FORMALISM | THREADING DECOMPOSITION OF THE METRIC PERTURBATIONS | GAUGE TRANSFORMATION OF THE FIELD VARIABLES | GAUGE-INVARIANT SCALARS | FIELD EQUATIONS FOR THE SCALAR PERTURBATIONS | FIELD EQUATIONS FOR VECTOR PERTURBATIONS | FIELD EQUATIONS FOR TENSOR PERTURBATIONS | RESIDUAL GAUGE FREEDOM | POST-NEWTONIAN FIELD EQUATIONS IN A SPATIALLY FLAT UNIVERSE | COSMOLOGICAL PARAMETERS AND SCALAR FIELD POTENTIAL | CONFORMAL COSMOLOGICAL PERTURBATIONS | POST-NEWTONIAN FIELD EQUATIONS IN CONFORMAL SPACETIME | RESIDUAL GAUGE FREEDOM IN THE CONFORMAL SPACETIME | DECOUPLED SYSTEM OF THE POST-NEWTONIAN FIELD EQUATIONS | THE UNIVERSE GOVERNED BY DARK MATTER AND COSMOLOGICAL CONSTANT | THE UNIVERSE GOVERNED BY DARK ENERGY | POST-NEWTONIAN POTENTIALS IN THE LINEARIZED HUBBLE APPROXIMATION | LORENTZ INVARIANCE OF RETARDED POTENTIALS | RETARDED SOLUTION OF THE SOUND-WAVE EQUATION |