The Geometry of the Universe [1 ed.] 9789811233869, 9789811233876, 9789811233883

Table of contents :
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