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Gravity, Black Holes, and the Very Early Universe by Tai L. Chow

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Gravity, Black Holes, and the Very Early Universe, An Introduction to General Relativity and Cosmology written by Tai L. Chow , California State University Stanislaus, Turlock, CA, USA This is an other great mathematics book cover the following topics.

  • 1 Basic Ideas of General Relativity
    1.1 Inadequacy of Special Relativity
    1.2 Einstein’s Principle of Equivalence
    1.3 Immediate Consequences of the Principle of Equivalence
    1.3.1 The Bending of a Light Beam
    1.3.2 Gravitational Shift of Spectral Lines (Gravitational Redshift)
    1.4 The Curved Space-Time Concept
    1.5 The Principle of General Covariance
    1.6 Distance and Time Intervals
    1.7 Problems

  • 2 Curvilinear Coordinates and General Tensors
    2.1 Curvilinear Coordinates
    2.2 Parallel Displacement and Covariant Differentiation
    2.3 Symmetry Properties of the Christoffel Symbols
    2.4 Christoffel Symbols and theMetric Tensor
    2.5 Geodesics
    2.6 The Stationary Property of Geodesics
    2.7 The Curvature Tensor
    2.8 The Condition for Flat Space
    2.9 Geodesic Deviation
    2.10 Laws of Physics in Curved Spaces
    2.11 The Metric Tensor and the Classical Gravitational Potential
    2.12 Some Useful Calculation Tools
    2.13 Problems

  • 3 Einstein’s Law of Gravitation
    3.1 Introduction (Summary of General Principles)
    3.2 A Heuristic Derivation of Einstein’s Equations
    3.2.1 Vacuum Field Equations
    3.2.2 Field Equations Where Matter is Present in Space
    3.3 Energy-Momentum Tensor
    3.4 Gravitational Radiation
    3.5 Problems

  • 4 The Schwarzschild Solution
    4.1 The Schwarzschild Metric
    4.2 The Schwarzschild Solution of the Vacuum Field Equations
    4.3 Schwarzschild Geodesics
    4.4 Quasiuniform Gravitational Field
    4.5 Problems

  • 5 Experimental Tests of Einstein’s Theory
    5.1 Precession of the Perihelion ofMercury
    5.2 Deflection of Light Rays in a Gravitational Field
    5.3 Light Retardation (The Shapiro Experiment)
    5.4 Test of Gravitational Radiation (Hulse-Taylor’s Measurement of the Orbital Decay of the Binary Pulsar PSR-1913+16)
    5.5 Problems

  • 6 The Physics of Black Holes
    6.1 The Schwarzschild Black Hole
    6.2 Inside a Black Hole
    6.3 How a Black HoleMay Form
    6.4 The Kerr-Newman Black Hole
    6.4.1 Energy Extraction from a Rotating Black Hole: The Penrose Process
    6.4.2 The Area Theorem
    6.4.3 Energy Extraction from Two Coalescing Black Holes
    6.5 Thermodynamics of Black Holes
    6.6 Quantum Mechanics of Black Holes: Hawking Radiation
    6.7 The Detection of Black Holes
    6.7.1 Detection of Stellar-Mass Black Holes
    6.7.2 Supermassive Black Holes in the Centers of Galaxies
    6.7.3 Intermediate-Mass Black Holes
    6.8 How Do Electrical and Gravitational Fields Get Out of Black Holes?. 106
    6.9 Black Holes and Particle Physics
    6.10 Problems

  • 7 Introduction to Cosmology
    7.1 Introduction
    7.2 The Development of Western Cosmological Concepts
    7.2.1 Ancient Greece
    7.2.2 The Renaissance of Cosmology
    7.2.3 Newton and the Infinite Universe .
    7.2.4 Newton’s Law of Gravity and a Nonstationary Universe
    7.2.5 Olbers’ Paradox
    7.3 The Discovery of the Expansion of the Universe
    7.4 The Big Bang.
    7.5 The Microwave Background Radiation
    7.6 Additional Evidence for the Big Bang
    7.7 Problems

  • 8 Big Bang Models
    8.1 The Cosmic Fluid and Fundamental Observers
    8.2 Properties of the Robertson-Walker Metric
    8.3 Cosmic Dynamics and Friedmann’s Equations
    8.4 The Solutions of Friedmann’s Equations
    8.4.1 Flat Model (k = 0)
    8.4.2 Closed Model (k = 1)
    8.4.3 Open Model (k = −1)
    8.5 DarkMatter and the Fate of the Universe
    8.6 The Beginning, the End, and Time’s Arrow
    8.7 An Accelerating Universe?
    8.8 The Cosmological Constant
    8.9 Problems

  • 9 Particles, Forces, and Unification of Forces
    9.1 Particles
    9.1.1 Spin
    9.1.2 Fermions
    9.1.3 Bosons
    9.1.4 Hadrons and Leptons
    9.1.5 Quarks
    9.1.6 Quark Colors
    9.1.7 Quark Confinement
    9.2 Fundamental Interactions and Conservation Laws
    9.3 Spontaneous Symmetry Breaking
    9.4 Unification of Forces (Interactions)
    9.5 The Negative Vacuum Pressure

  • 10 The Inflationary Universe
    10.1 The Flatness Problem
    10.2 The Horizon Problem
    10.3 Alan Guth’s Inflationary Theory
    10.4 The Successes of Guth’s Inflationary Theory
    10.4.1 The Horizon Problem Resolved
    10.4.2 The Flatness Problem Resolved
    10.5 Problems with Guth’s Theory and the New Inflationary Theory
    10.6 Problems

  • 11 The Physics of the Very Early Universe
    11.1 Introduction
    11.2 Cosmic Background Radiation
    11.2.1 Conservation of Photon Numbers
    11.2.2 The Transition Temperature Tt
    11.2.3 The Photon-to-Baryon Ratio
    11.3 The Creation of Matter and Photons
    11.4 A Brief History of the Early Universe
    11.4.1 The Planck Epoch
    11.4.2 The GUTs Era
    11.4.3 The Inflationary Era
    11.4.4 The Hadron Era
    11.4.5 The Lepton Era
    11.4.6 The Nuclear Era
    11.5 TheMystery of Antimatter
    11.6 The DarkMatter Problem
    11.7 The Primordial Magnetic Fields
    11.8 Problems

  • A Classical Mechanics
    A.1 Newtonian Mechanics
    A.1.1 The Three Laws ofMotion
    A.1.2 The Galilean Transformation
    A.1.3 Newtonian Relativity and Newton’s Absolute Space
    A.1.4 Newton’s Law of Gravity
    A.1.5 Gravitational Mass and Inertial Mass
    A.1.6 Gravitational Field and Gravitational Potential
    A.1.7 Gravitational Field Equations
    A.2 Lagrangian Mechanics
    A.2.1 Hamilton’s Principle
    A.2.2 Lagrange’s Equations of Motion
    A.3 Problems

  • B The Special Theory of Relativity
    B.1 The Origins of Special Relativity
    B.2 The Michelson-Morley Experiment
    B.3 The Postulates of the Special Theory of Relativity
    B.4 The Lorentz Transformations
    B.4.1 Relativity of Simultaneity and Causality
    B.4.2 Time Dilation and Relativity of Co-locality
    B.4.3 Length contraction
    B.4.4 Velocity Transformation
    B.5 The Doppler Effect
    B.6 Relativistic Space-Time and Minkowski Space
    B.6.1 Interval ds2 as an Invariant
    B.6.2 Four Vectors
    B.6.3 Four-Velocity and Four-Acceleration
    B.6.4 Four-Momentum Vector
    B.6.5 The Conservation Laws of Energy and Momentum
    B.6.6 Equivalence of Mass and Energy
    B.7 Problems

  • References

  • Index

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