A College Course on Relativity and Cosmology

• Main Author: Cheng, Ta-Pei
• Format: eBook Book
• Language: English
• Published: Oxford Oxford University Press 2015; Oxford University Press, Incorporated
• Edition: 1
• Subjects: Astronomy and Astrophysics; Cosmology; Gravity; Relativity (Physics); Specific celestial bodies & phenomena; spacetime; Einstein; black hole; gravitation; Schwarzschild; relativity; cosmology; light deflection; tensor; equivalence principle

This book introduces Einstein’s general theory of relativity. Topics include the geometric formulation of special relativity, the principle of equivalence, the Einstein field equation and its spherical solution, and black holes, as well as cosmology. The subject is presented with an emphasis on phys...

Table of Contents:

• Appendix A Keys to Review Questions -- Appendix B Hints for Selected Exercises -- Appendix C Glossary of Symbols and Acronyms -- References and Bibliography -- Index
• 8.2 The homogeneous and isotropic universe -- 8.2.1 Robertson-Walker metric in comoving coordinates -- 8.2.2 Hubble's law follows from the cosmological principle -- 8.3 Time evolution in FLRW cosmology -- 8.3.1 Friedmann equations and their simple interpretation -- 8.3.2 Time evolution of model universes -- 8.4 The cosmological constant Λ -- 8.4.1 Λ as vacuum energy and pressure -- 8.4.2 Λ-dominated universe expands exponentially -- Review questions -- 9 Big Bang Thermal Relics -- 9.1 The thermal history of the universe -- 9.1.1 Scale dependence of radiation temperature -- 9.1.2 Different thermal equilibrium stages -- 9.2 Primordial nucleosynthesis -- 9.3 Photon decoupling and cosmic microwave background -- 9.3.1 Universe became transparent to photons -- 9.3.2 CMB anisotropy as a baby picture of the universe -- Review questions -- 10 Inflation and the Accelerating Universe -- 10.1 The cosmic inflation epoch -- 10.1.1 Initial condition problems of FLRW cosmology -- 10.1.2 The inflationary scenario -- 10.1.3 Eternal inflation and the multiverse -- 10.2 The accelerating universe in the present era -- 10.2.1 Dark energy and its effect -- 10.2.2 Distant supernovae and the 1998 discovery -- 10.2.3 The mysterious physical origin of dark energy -- 10.3 ΛCDM cosmology as the standard model -- Review questions -- 11 Tensor Formalism for General Relativity -- 11.1 Covariant derivatives and parallel transport -- 11.1.1 Derivatives in a curved space and Christoffel symbols -- 11.1.2 Parallel transport and geodesics as straight lines -- 11.2 Riemann curvature tensor -- 11.2.1 Parallel transport of a vector around a closed path -- 11.2.2 Equation of geodesic deviation -- 11.2.3 Bianchi identity and the Einstein tensor -- 11.3 GR tensor equations -- 11.3.1 The principle of general covariance -- 11.3.2 Einstein field equation -- Review questions
• 4.3.4 Energetics of light transmission in a gravitational field -- Review questions -- 5 General Relativity as a Geometric Theory of Gravity -- 5.1 Metric description of a curved manifold -- 5.1.1 Gaussian coordinates and the metric tensor -- 5.1.2 The geodesic equation -- 5.1.3 Local Euclidean frames and the flatness theorem -- 5.2 From the equivalence principle to a metric theory of gravity -- 5.2.1 Curved spacetime as gravitational field -- 5.2.2 GR as a field theory of gravitation -- 5.3 Geodesic equation as the GR equation of motion -- 5.3.1 The Newtonian limit -- Review questions -- 6 Einstein Equation and its Spherical Solution -- 6.1 Curvature: a short introduction -- 6.2 Tidal gravity and spacetime curvature -- 6.2.1 Tidal forces-a qualitative discussion -- 6.2.2 Deviation equations and tidal gravity -- 6.3 The GR field equation -- 6.3.1 Einstein curvature tensor -- 6.3.2 Einstein field equation -- 6.3.3 Gravitational waves -- 6.4 Geodesics in Schwarzschild spacetime -- 6.4.1 The geometry of a spherically symmetric spacetime -- 6.4.2 Curved spacetime and deflection of light -- 6.4.3 Precession of Mercury's orbit -- Review questions -- 7 Black Holes -- 7.1 Schwarzschild black holes -- 7.1.1 Time measurements around a black hole -- 7.1.2 Causal structure of the Schwarzschild surface -- 7.1.3 Binding energy to a black hole can be extremely large -- 7.2 Astrophysical black holes -- 7.2.1 More realistic black holes -- 7.2.2 Black holes in our universe -- 7.3 Black hole thermodynamics and Hawking radiation -- 7.3.1 Laws of black hole mechanics and thermodynamics -- 7.3.2 Hawking radiation: quantum fluctuation around the horizon -- Review questions -- 8 The General Relativistic Framework for Cosmology -- 8.1 The cosmos observed -- 8.1.1 The expanding universe and its age -- 8.1.2 Mass/energy content of the universe
• Intro -- A College Course on Relativity and Cosmology -- Copyright -- Dedication -- Preface -- Contents -- 1 Introduction -- 1.1 Relativity as a coordinate symmetry -- 1.1.1 Coordinate transformations -- 1.1.2 The principle of relativity -- 1.2 Einstein and relativity -- 1.2.1 The new kinematics -- 1.2.2 GR as a field theory of gravitation -- Review questions -- 2 Special Relativity: The New Kinematics -- 2.1 Einstein's two postulates and Lorentz transformation -- 2.1.1 Relativity of simultaneity and the new conception of time -- 2.1.2 Coordinate-dependent time leads to Lorentz transformation -- 2.2 Physics implications of Lorentz transformation -- 2.2.1 Time dilation and length contraction -- 2.2.2 The invariant interval and proper time -- 2.3 Two counterintuitive scenarios as paradoxes -- Review questions -- 3 Special Relativity: Flat Spacetime -- 3.1 Geometric formulation of relativity -- 3.2 Tensors in special relativity -- 3.2.1 Generalized coordinates: bases and the metric -- 3.2.2 Velocity and momentum 4-vectors -- 3.2.3 Electromagnetic field 4-tensor -- 3.2.4 The energy-momentum-stress 4-tensor for a field system -- 3.3 The spacetime diagram -- 3.3.1 Invariant regions and causal structure -- 3.3.2 Lorentz transformation in the spacetime diagram -- Review questions -- 4 Equivalence of Gravitation and Inertia -- 4.1 Seeking a relativistic theory of gravitation -- 4.1.1 Newtonian potential: a summary -- 4.1.2 Einstein's motivation for general relativity -- 4.2 The equivalence principle: from Galileo to Einstein -- 4.2.1 Inertial mass vs. gravitational mass -- 4.2.2 Einstein: "my happiest thought" -- 4.3 EP leads to gravitational time dilation and light deflection -- 4.3.1 Gravitational redshift and time dilation -- 4.3.2 Relativity and the operation of GPS -- 4.3.3 The EP calculation of light deflection