Introduction to general relativity 1st Edition by Lewis Ryder ISBN 0521845637 9780521845632

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ISBN 10: 0521845637 
ISBN 13: 9780521845632
Author: Lewis Ryder

A student-friendly style, over 100 illustrations, and numerous exercises are brought together in this textbook for advanced undergraduate and beginning graduate students in physics and mathematics. Lewis Ryder develops the theory of general relativity in detail. Covering the core topics of black holes, gravitational radiation, and cosmology, he provides an overview of general relativity and its modern ramifications. The book contains chapters on gravitational radiation, cosmology, and connections between general relativity and the fundamental physics of the microworld. It explains the geometry of curved spaces and contains key solutions of Einstein’s equations – the Schwarzschild and Kerr solutions. Mathematical calculations are worked out in detail, so students can develop an intuitive understanding of the subject, as well as learn how to perform calculations. The book also includes topics concerned with the relation between general relativity and other areas of fundamental physics. Selected solutions for instructors are available under Resources.

Introduction to general relativity 1st Table of contents:

1 Introduction
1.1 The need for a theory of gravity
1.2 Gravitation and inertia: the Equivalence Principle in mechanics
1.1.1 A remark on inertial mass
1.1.2 Tidal forces
1.3 The Equivalence Principle and optics
1.4 Curved surfaces
Further reading
Problems
2 Special Relativity, non-inertial effects and electromagnetism
2.1 Special Relativity: Einstein’s train
2.1.1 Minkowski space-time
2.1.2 Lorentz transformations
2.2 Twin paradox: accelerations
2.3 Rotating frames: the Sagnac effect
2.3.1 Clock synchronisation
2.4 Inertia: Newton versus Mach
2.5 Thomas precession
2.6 Electromagnetism
2.6.1 Maxwell’s equations
2.7 Principle of General Covariance
Further reading
Problems
3 Differential geometry I: vectors, differential forms and absolute differentiation
3.1 Space-time as a differentiable manifold
3.2 Vectors and vector fields
3.2.1 Holonomic and anholonomic bases
3.3 One-forms
3.3.1 Transformation rules
3.3.2 A note on orthogonal coordinate systems
3.4 Tensors
3.4.1 Contraction
3.4.2 Symmetry and antisymmetry
3.4.3 Quotient theorem
3.5 Differential forms: Hodge duality
3.5.1 Remarks on the algebra of p-forms
3.5.2 A note on orientation
3.6 Exterior derivative operator: generalised Stokes’ theorem
3.6.1 Generalised Stokes’ theorem
3.6.2 Closed and exact forms
3.7 Maxwell’s equations and differential forms
3.8 Metric tensor
3.8.1 Holonomic and anholonomic (coordinate and non-coordinate) bases
3.8.2 Tensor densities: volume elements
3.9 Absolute differentiation: connection forms
3.9.1 Tensors
3.10 Parallel transport
3.11 Some relations involving connection coefficients
3.11.1 Derivatives of scalar and tensor densities
3.11.2 Note on torsion and curvature
3.12 Examples
3.12.1 Plane E: coordinate basis
3.12.2 Sphere S
3.13 General formula for connection coefficients
Further reading
Problems
4 Differential geometry II: geodesics and curvature
4.1 Autoparallel curves and geodesics
4.1.1 Autoparallel curves
4.1.2 Geodesics
4.1.3 Examples
4.2 Geodesic coordinates
4.3 Curvature
4.3.1 Round trips by parallel transport
4.4 Symmetries of the Riemann tensor
4.5 Ricci tensor and curvature scalar
4.5.1 Plane and sphere: holonomic basis
4.5.2 Plane and sphere: anholonomic basis
4.6 Curvature 2-form
4.7 Geodesic deviation
4.8 Bianchi identities
Further reading
Problems
5 Einstein field equations, the Schwarzschild solution and experimental tests of General Relativity
5.1 Newtonian limit
5.2 Einstein field equations
5.2.1 Vacuum field equations
5.2.2 Energy-momentum tensor
5.2.3 Matter field equations
5.3 Schwarzschild solution
5.3.1 Apparent ‘singularity’ at r = 2m
5.3.2 Isotropic form of the Schwarzschild solution
5.4 Time dependence and spherical symmetry: Birkhoff’s theorem
5.5 Gravitational red-shift
5.6 Geodesics in Schwarzschild space-time
5.7 Precession of planetary orbits
5.8 Deflection of light
5.9 Note on PPN formalism
5.10 Gravitational lenses
5.11 Radar echoes from planets
5.12 Radial motion in a Schwarzschild field: black holes – frozen stars
5.13 A gravitational clock effect
Further reading
Problems
6 Gravitomagnetic effects: gyroscopes and clocks
6.1 Linear approximation
6.1.1 Static case: mass
6.1.2 Rotating body: angular momentum
6.2 Precession of gyroscopes: the Lense–Thirring effect
6.2.1 Gravity Probe B
6.2.2 ‘Inertial drag’
6.2.3 Lense–Thirring effect and Mach’s Principle
6.3 Gravitomagnetism
6.4 Gravitomagnetic clock effect
6.5 Fermi–Walker transport: tetrad formalism
6.6 Lie derivatives, Killing vectors and groups of motion
6.6.1 Groups of motion
6.7 Static and stationary space-times
6.8 Killing vectors and conservation laws
Further reading
Problems
7 Gravitational collapse and black holes
7.1 The interior Schwarzschild solution and the Tolman–Oppenheimer–Volkoff equation
7.2 Energy density and binding energy
7.3 Degenerate stars: white dwarfs and neutron stars
7.4 Schwarzschild orbits: Eddington–Finkelstein coordinates
7.5 Kruskal–Szekeres coordinates
7.6 Einstein–Rosen bridge and wormholes
7.7 Conformal treatment of infinity: Penrose diagrams
7.8 Rotating black holes: Kerr solution
7.9 The ergosphere and energy extraction from a black hole
7.10 Surface gravity
7.11 Thermodynamics of black holes and further observations
7.12 Global matters: singularities, trapped surfaces and Cosmic Censorship
Further reading
Problems
8 Action principle, conservation laws and the Cauchy problem
8.1 Gravitational action and field equations
8.2 Energy-momentum pseudotensor
8.3 Cauchy problem
Further reading
Problems
9 Gravitational radiation
9.1 Weak field approximation
9.1.1 Spin 2 graviton
9.1.2 The effect of gravitational waves
9.2 Radiation from a rotating binary source
9.2.1 Flux
9.2.2 Radiated energy
9.2.3 Spin-up and the binary pulsar PSR 1913+16
9.2.4 Search for gravitational waves
9.3 Parallels between electrodynamics and General Relativity: Petrov classification
9.3.1 A geometric approach to electrodynamics
9.3.2 Petrov classification
Further reading
Problems
10 Cosmology
10.1 Brief description of the Universe
10.2 Robertson–Walker metric
10.3 Hubble’s law and the cosmological red-shift
10.4 Horizons
10.5 Luminosity–red-shift relation
10.6 Dynamical equations of cosmology
10.6.1 Newtonian interpretation
10.6.2 Critical density
10.7 Friedmann models and the cosmological constant
10.8 Cosmic background radiation
10.9 Brief sketch of the early Universe
10.10 The inflationary universe and the Higgs mechanism
Further reading
Problems
11 Gravitation and field theory
11.1 Electrodynamics as an abelian gauge theory
11.2 Non-abelian gauge theories
11.3 Gauging Lorentz symmetry: torsion
11.4 Dirac equation in Schwarzschild space-time
11.5 Five dimensions: gravity plus electromagnetism

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