The Geometry of the Universe (Series on Knots and Everything, 71)

"Cosmology, the study of the universe, arouses a great deal of public interest, with serious articles both in the scientific press and in major newspapers, with many of the theories and concepts (e.g. the "big bang" and "black holes") discussed, often in great depth. Accordingly the book is divided into three parts: Part 1: The whole story presented as far as possible for a nontechnical reader Part 2: The same story, told again but for a reader with some technical knowledge Part 3: Appendices with full technical details of several of the important topics covered. Part 1 is readable (and understandable) by anyone with a nodding acquaintance with the basic language of cosmology: events, lights paths, galaxies, black holes and so on. It covers the whole story of the book in a way as untechnical as possible given the scope of the topics covered. Part 2 covers the same ground again but with enough technical details to satisfy a reader with basic knowledge of mathematics and/or physics. Part 3 consists of appendices which are referred to in the other parts and which also contain the highly technical material omitted from Section 2"-- Provided by publisher Contents Foreword About the author Table of contents PART 1 1 From the Greeks to Einstein 1.1 Kepler and Newton Kepler’s laws of planetary motion 1.2 Newtonian physics: gravitation and dynamics Newton’s laws of motion Newton’s law of gravitation 1.3 Derivation of Kepler’s laws 2 and 3 Angular momentum 1.4 Maxwell and the road to Special Relativity The æther and the Michelson–Morley experiments 2 Einstein, relativity, model building and de Sitter 2.1 Special Relativity 2.2 General Relativity 2.3 Model building Einstein’s “biggest blunder” 2.4 de Sitter space de Sitter space and Mach’s principle 3 The biggest blunder, dark matter and quasars 3.1 The biggest blunder Weyl’s postulate De Sitter space as a model for the universe 3.2 The standard model Two philosophical problems 3.3 Dark matter Sciama’s principle and inertial drag The rotation curve The fundamental relation Spiral structure 3.4 The Arp problem 3.5 The quasar–galaxy spectrum 3.6 Killing the angular momentum obstruction 3.7 Embedding Mach’s principle in EGR 3.8 Outline of Part 2 PART 2 4 Sciama’s principle 4.1 Inertial frames and Mach’s principle 4.2 Sciama’s principle 4.3 An excerpt from Mach’s critique 4.4 Rotation 4.5 The weak Sciama principle 4.6 The Lense–Thirring effect 4.7 Central rotation 4.8 Adding Sciama’s principle to EGR 4.9 Sciama’s principle and black holes 4.10 Coda 5 The rotation curve 5.1 The weak Sciama principle 5.2 The dynamical effect of the inertial drag field 5.3 A metrical interpretation of inertial drag 5.4 Conservation of angular momentum 5.5 The fundamental relation 5.6 Solving to find rotation curves 5.7 The basic model 5.8 Postscript 6 Quasars 6.1 Angular momentum and inertial drag 6.2 Outline of the threeauthormodel 6.3 Three important spheres 6.4 Previous work on quasars and gravitational red shift 7 Spiral structure 7.1 Introduction 7.2 The generator 7.3 The full dynamic 7.4 Computing radial velocity 7.5 Simplified equations 7.6 Mathematica generated pictures 7.7 The bulge 7.8 Bar galaxies 8 Observations 8.1 21cm emission observations 8.2 Stellar populations 8.3 Sagittarius A* 8.4 Where is the Sun? 8.5 Globular clusters 8.6 Local stellar velocities 9 Cosmology 9.1 The Big Bang? 9.2 The distribution of light elements 9.3 De Sitter space Expansion Contraction 9.4 Redshift 9.5 Cosmic microwave background The gravitational fog horizon: a limit to visibility The HLSW constant: a crisis in Physics Horizon effect and dipole anisotropy Quantum fluctuations? The multipole power spectrum 9.6 Redshift and GRBs revisited 9.7 Origin of life 9.8 The quasar–galaxy spectrum The Hawkins paper Quasars and redshift Quasars and active galaxies Active and spiral galaxies The predominant lifeformof the universe The lords of the universe PART 3 A Introduction to relativity A.1 Causality A.2 The speed of light and Michelson–Morley A.3 Lorentz transformations A.4 Time dilation and length contraction A.5 Minkowski space A.6 General Relativity A.7 Manifolds and spacetimes A.8 Curvature Riemann curvature Ricci curvature A.9 Einstein’s equations Einstein’s biggest blunder Vacuum equations with cosmological constant The Schwarzschild and de Sitter solutions Black holes De Sitter space B De Sitter space B.1 Minkowski space B.2 Spacetimes B.3 de Sitter and hyperbolic spaces B.4 Projective geometry B.5 Hyperbolic and de Sitter geometry B.6 Transitivity of points and geodesics B.7 The expansive metric B.8 Timelikegeodesics in Exp B.9 The de Sitter metric B.10 Explicit formulae C Quasars: technical material C.1 Bondi sphere radius and accretion rate C.2 Kinetic energy, escape velocity and redshift C.3 Potential and kinetic energy in Schwarzschild space-time C.4 The critical radius and high redshift black holes C.5 Calculations Redshift in terms of medium factor and mass Three types of redshift and the HLSW formula Luminosity and magnitude Eddington radius Radiant temperature C.6 Data C.7 Conclusions D Local stellar velocities D.1 The observations D.2 The explanations: Velocity variation increases with age D.3 Asymmetric drift D.4 Vertex deviation E Optical distortion in the Hubble UltraDeepField E.1 Introduction E.2 The face galaxy E.3 Gravitational solitons E.4 The companion face E.5 The group of four E.6 Four distorted spirals E.7 Miscellanea E.8 Conclusion F Gamma Ray Bursts F.1 Introduction F.2 Geodesics in de Sitter space F.3 Critique F.4 Final remark Bibliography Index Cosmology, the universe, arouses a great deal of public interest, with serious articles both in the scientific press and in major newspapers, with many of the theories and concepts (e. g. the "Big Bang" and "black holes") discussed, often in great depth. The observation that support these discussions use sophisticated and expensive machinery both on the earth (e. g. the LIGO equipment used to detect gravitational waves) and in orbit around the earth (e. g. the Hubble telescope). There is a consensus for the theoretical framework interpreting these observations, which is known as the "standard model". This starts with a singular event known as the "Big Bang" and expands from there to fill the entire visible universe. The image presented is of a complete and full theory that (with a few minor unsolved problems) explains all the observations that we have. This image is (like many images) complete ly false. There are huge problems with the standard model and it is the aim of this book to present a new model, which avoids these problems. The model is based on a geometric description of the universe and hence the title. In this new model there is no Big Bang and no dark matter