A college course on relativity and cosmology / Ta-Pei Cheng

Author:: Cheng, Ta-Pei
Published:: Oxford : Oxford University Press, 2015.
Edition:: First edition.
Physical Description:: 1 online resource : illustrations (black and white)

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Contents:

Machine generated contents note: 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 -- 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.Geodesies 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 -- 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 Δ -- 8.4.1.Δ as vacuum energy and pressure -- 8.4.2.Δ-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.ΔCDM 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 geodesies 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.

Summary:

Einstein's general theory of relativity is introduced in this advanced undergraduate textbook. Topics covered include geometric formulation of special relativity, the principle of equivalence, Einstein's field equation and its spherical-symmetric solution, as well as cosmology.

Subject(s):

ISBN:

9780191803130 (ebook)

Bibliography Note:

Includes bibliographical references and index.

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