General Relativity and Cosmology: A First Encounter (Graduate Texts in Physics)

Preface
Contents
Part ISpecial Relativity in Review
1 A Brief Stroll in Special Relativity
	1.1 The Trouble with Absolute Time
	1.2 The Simplest Lorentz Transformation
	1.3 Some Elementary Properties and Applications
2 Lorentz Transformations
	2.1 The Lorentz Group
	2.2 Four-Vectors and Tensors
3 The Motion of Particles
	3.1 Energy and Momentum
	3.2 Acceleration
	3.3 Accelerated Motion
	3.4 Curves and Arc Lengths
Part IIVectors and Tensors
4 Riemann Spaces and Tensors
	4.1 Riemann Spaces
	4.2 Vectors, Component View
	4.3 Vectors and 1-Forms, Abstract View
	4.4 Tensors, Component View
	4.5 Tensors, Abstract View
	4.6 Tetrads and n-Trads
	4.7 Volume Elements
	Appendix 1: Differential Manifolds
	Appendix 2: The Signature Theorem in Two Dimensions
5 Affine Connections and Geodesics
	5.1 Affine Connections, Component View
	5.2 Transformation of the Affine Connections
	5.3 Parallel Displacement
	5.4 Geodesics as Self-parallel Curves
	5.5 Geodesics as Extremum Curves
	5.6 Affine Connections, Abstract View
	Appendix 1: A Special Coordinate System
	Appendix 2: The Extremum Problem and the Euler-Lagrange Equations
	Appendix 3: Christoffel Connections as Fictitious Forces
6 Tensor Analysis
	6.1 Covariant Derivatives, Component View
	6.2 Covariant Derivatives, Abstract View
	6.3 The Divergence and Laplacian
	Appendix 1: Curve Derivatives as Vectors
	Appendix 2: p-Forms and Exterior Derivatives
Part IIIGeneral Relativity
7 Classical Gravity and Geometry
	7.1 Newtonian Gravity
	7.2 The Equivalence Principle
	7.3 Gravity as a Geometric Phenomenon
8 Curved Space and Gravity
	8.1 Curved Space and the Riemann Tensor
	8.2 Symmetries of the Riemann Tensor
	8.3 The Einstein Equations for the Gravitational Field in Vacuum
	8.4 The Non-vacuum Field Equations
	8.5 The Intrinsic Signature of Gravity
	Appendix 1: Tangent Spaces
	Appendix 2: The Riemann Tensor as a 6 by 6 Matrix
9 Spherically Symmetric Gravitational Fields
	9.1 The Schwarzschild Solution
	9.2 Orbit of a Planet
	9.3 Deflection of Light
	9.4 Observational Tests of General Relativity
	Appendix 1: Isotropic Form of the Metric, Eddington Parameters
10 Black Holes and Gravitational Collapse
	10.1 Schwarzschild Black Hole
	10.2 Null Surfaces
	10.3 Stellar Evolution, Very Briefly
	10.4 Collapse of a Dust Star
	10.5 Spinning Black Holes and the Kerr Metric
	10.6 Black Holes in the Real Universe
	10.7 Hawking Radiation from a Black Hole
11 Linearized General Relativity and Gravitational Waves
	11.1 The Field Equations of the Linearized Theory
	11.2 The Classical Limit
	11.3 Gravitational Plane Waves
	11.4 Motion of Test Bodies in Gravitational Waves
	11.5 Gravitational Wave Sources
	11.6 Detection of Gravitational Waves
	Appendix 1: Solutions for Retarded Potentials
	Appendix 2: Electromagnetic Plane Waves
	Appendix 3: Electromagnetic Wave Sources
Part IVCosmology
12 The Einstein Field Equations for Cosmology
	12.1 The Field Equations and Energy-Momentum Conservation
	12.2 Field Equations and the Cosmic Fluid Source
	12.3 The Cosmological Constant as Vacuum or Dark Energy
	12.4 Summary
13 Cosmological Preliminaries
	13.1 Basic Observations and Assumptions
	13.2 The Cosmological FLRW Metric
	13.3 Consequences of the Metric
	13.4 De Sitter Space
	Appendix 1: Measured Values for the Hubble Constant
14 The Dynamical Equations of Cosmology
	14.1 The Einstein Field Equations for Cosmology
	14.2 Critical Density and the Shape of the Universe
	14.3 Observed Dark Matter and Dark Energy Densities
	14.4 Evolution of Cosmic Fluid Constituents
	14.5 The Friedmann Master Equation
	Appendix 1: The Einstein Tensor for the FLRW Metric
15 Solutions for the Present Universe
	15.1 The Positive Cosmological Constant
	15.2 Complete Solution of the Friedmann Master Equation
	15.3 Cosmological Constant Dominance
	15.4 Matter Dominance
	15.5 The LCDM Universe
	Appendix 1: A Mechanical Analogy
	Appendix 2: Newtonian View of Dark Energy
	Appendix 3: Some Discarded Cosmological Models
16 Some Properties of the LCDM Universe
	16.1 Diverse Cosmological Observations
	16.2 Cosmological Parameter Values
	16.3 The Hubble Function and the Age of the Universe
	16.4 Transition Time for Matter to Dark Energy Dominance
	16.5 Density Ratios and the Shape of the Universe
	16.6 Horizons and the Size of the Observable Universe
	16.7 Conformal Time
17 Earlier Times and Radiation
	17.1 Radiation and Temperature in Earlier Times
	17.2 The Scale Factor and Basic Properties of the Radiation Era
	17.3 The Isotropic CMB and the Horizon Puzzle
	17.4 The Anisotropies of the CMB
18 A Brief Historical Overview of the Universe
	18.1 Overview
	18.2 Condensation of Stars and Galaxies
	18.3 Condensation of Atoms
	18.4 Condensation of Nuclei
	18.5 Condensation of Nucleons
	18.6 Inflation
	18.7 Planck Era
19 Inflation and Some Questions
	19.1 Basic Ideas of Inflation
	19.2 Inflation Via Scalar Fields
	19.3 Origin of Structure
	19.4 The Physical Nature of Dark Energy
	19.5 The Physical Nature of Dark Matter
	19.6 The Planck Era and Quantum Physics
	Appendix 1: Power Law Inflation
	Appendix 2: Scalar Field Theory
	Appendix 3: Black Hole Remnants as Dark Matter
References
Index