PROBLEMS OF COSMOGONY AND STELLAR DYNAMICS

By JOHN SMITH

CONTENTS INTRODUCTION PART I BKL ANALYSIS BASIC STRUCTURE OF COSMOLOGICAL SINGULARITY SYNCHRONOUS REFERENCE SYSTEM THE GRAVITATIONAL FIELD EQUATIONS GENERAL SOLUTION DE?NITION OF COSMOLOGICAL SINGULARITY KASNER-LIKE SINGULARITIES OF POWER LAW ASYMPTOTICS INSTABILITY OF KASNER DYNAMICS TRANSITION TO THE NEW REGIME OSCILLATORY NATURE OF THE GENERIC SINGULARITY ROTATION OF KASNER AXES FINAL COMMENTS HOMOGENEOUS COSMOLOGICAL MODELS HOMOGENEOUS MODELS OF BIANCHI TYPES IX AND VIII EQUATIONS OF MOTION FOR HOMOGENEOUS MODELS MODELS OF TYPES IX AND VIII WITH FIXED KASNER AXES MODELS OF TYPES IX AND VIII WITH ROTATING AXES ON THE EXTENSION TO THE INHOMOGENEOUS CASE ON THE COSMOLOGICAL CHAOS STOCHASTICITY OF THE OSCILLATORY REGIME HISTORICAL REMARKS GRAVITATIONAL TURBULENCE CONTENTS ON THE IN?UENCE OF MATTER AND SPACE-TIME DIMENSION INTRODUCTION PERFECT FLUID PERFECT FLUID OF STI?MATTER EQUATION OF STATE YANG–MILLS AND ELECTROMAGNETIC FIELDS SCALAR FIELD PURE GRAVITY IN HIGHER DIMENSIONS GENERALIZED KASNER SOLUTIONS: RIGOROUS RESULTS ON THE IN?UENCE OF VISCOUS MATTER PART II COSMOLOGICAL BILLIARDS THE BILLIARD OF FOUR-DIMENSIONAL VACUUM GRAVITY HAMILTONIAN FORM OF THE ACTION SUPERMETRIC KASNER SOLUTION REVISITED HAMILTONIAN IN PSEUDO-GAUSSIAN GAUGE BKL LIMIT AND EMERGENCE OF BILLIARD DESCRIPTION COLLISION LAW MISCELLANEA CHAOS AND VOLUME OF THE BILLIARD TABLE COXETER GROUP FOR PURE GRAVITY IN FOUR DIMENSIONS GENERAL COSMOLOGICAL BILLIARDS MODELS – HAMILTONIAN FORM OF THE ACTION GEOMETRY OF THE SPACE OF SCALE FACTORS HYPERBOLIC SPACE IN M DIMENSIONS HAMILTONIAN IN IWASAWA VARIABLES AND BKL LIMIT WALLS CHAPTER 4 REVISITED HYPERBOLIC COXETER GROUPS CONVEX POLYHEDRA IN HYPERBOLIC SPACE COXETER GROUPS: GENERAL CONSIDERATIONS COXETER GROUPS: EXAMPLES COXETER GROUPS AND WEYL GROUPS COXETER GROUPS ASSOCIATED WITH GRAVITATIONAL THEORIES THE KAC–MOODY SYMMETRY CONJECTURE