| 0.07 | | Preface |
| 0.09 | | Notation |
| 0.11 | | Contents |
| 0.19 | | Copyright Acknowledgement |
| 1 | Part One | Preliminaries |
| 3 | 1 | Historical Introduction |
| 4 | 1 | History of Non-Euclidean Geometry |
| | | Euclid's Fifth Postulate |
| | | Alternative postulates of Proclos, Wallis, Legendre, Saccheri |
| | | Gauss, and non-Euclidean geometry |
| | | The geometry of Gauss, Bolyai, and Lobachevski |
| | | Klein's model |
| | | Inner properties of curved surfaces |
| | | Curvature determined from distances |
| | | The metric |
| | | Gaussian curvature |
| | | Riemmanian geometry |
| 11 | 2 | History of the Theory of Gravitation |
| | | alileo and falling bodies |
| | | Measurements of the ratio of gravitational and inertial mass, by Newton, Bessel, Eötvös, and Dicke |
| | | The inverse-square law |
| | | Newton's theory of gravitation |
| | | Anomalous precession of the perihelia of Mercury |
| | | Newcomb and Seeliger |
| 15 | 3 | History of the Principle of Relativity |
| | | Inertial frames in Newtonian mechanics |
| | | The Galileo group |
| | | Noninertial frames and absolute space |
| | | Newton's rotating bucket |
| | | Mach's principle |
| | | Inertial frames and rotation of the universe |
| | | Maxwell's equations not Galilean-invariant |
| | | The ether |
| | | The Michelson-Morley experiment |
| | | Lorentz invariance |
| | | Relativity restored by Einstein |
| | | The Principle of Equivalence |
| | | Scalar gravitational theories |
| | | Gravitation and the metric tensor |
| | | The General Theory of Relativity |
| 20 | | Bibliography |
| 21 | | References |
| 25 | 2 | Special Relativity |
| 25 | 1 | Lorents Transformations |
| | | The transformations defined |
| | | Invariant proper time |
| | | Invariant speed of light |
| | | Only LOrentz transformations leave the proper time invariant |
| | | Homogeneous, inhomogeneous, proper, improper Lorentz transforrmations |
| | | Rotations and boosts |
| 29 | 2 | Time Dilation |
| | | The special-relativistic dilation |
| | | The Döppler effect |
| 31 | 3 | Particle Dynamics |
| | | Relativistic force |
| | | The relativistic second law of motion |
| 32 | 4 | Energy and Momentum |
| | | The energy-momeentum four-vector |
| | | The nonrelativistic limit |
| | | Lorentz invariance of the conservation laws |
| | | Mass as a form of energy |
| 35 | 5 | Vectors and Tensors |
| | | Contravariant and covariant four-vectos |
| | | Raising and lowering indices |
| | | Gradients |
| | | Tensors |
| | | Linear combinations, direct products, contraction, differentiation |
| | | The Minkowski tensor |
| | | The Levi-Civita tensor |
| | | The zero tensor |
| | | Lorentz invariant equations |
| 39 | 6 | Currents and Densities |
| | | The current four-vector |
| | | Conservation |
| | | Constancy and Lorentz invariance of the total charge |
| 41 | 7 | Electrodynamics |
| | | The field-strenght tensor |
| | | Manifesty invariant forms of the Maxwell equations |
| 43 | 8 | Energy-Momentum Tensor |
| | | Enery-momentum tensor of point particles |
| | | The conservation law |
| | | Collisions |
| | | Charged particles |
| | | Energy-momentum tensor of electromagnetic fields |
| 46 | 9 | Spin |
| | | Total angular momentum |
| | | Internal and orbital angular momenta |
| | | The spin four-vector |
| 47 | 10 | Relativistic Hydrodynamics |
| | | Perfect fluids |
| | | Pressure and proper energy density |
| | | Energy-momentum tensor |
| | | Velocity four-vector |
| | | The particle current |
| | | Relativistic Euler equation |
| | | The entropy equation |
| | | Equations of state |
| | | Speed of sound |
| 53 | 11* | Relativistic Imperfect Fluids |
| | | The Eckart formalism |
| | | Entropy production |
| | | Heat conduction, shear viscosity, bulk viscosity |
| | | Lorentz covariant dissipative terms in the energy-momentum tensor |
| | | Cases of small bulk viscosity |
| 58 | 12* | representations of the Lorentz Group |
| | | Group representations |
| | | The infinitesimal Lorentz group |
| | | Commutation relations |
| | | The representations (A, B) |
| | | Tensors and spinors |
| | | Decomposition according to spin |
| | | Representations up to a sign |
| 61 | 13* | Temporal order and Antiparticles |
| | | The relativity of temporal order |
| | | Absorption before emission? |
| | | The quantum paradox |
| | | Antiparticles necessary in a relativistic quantum theory |
| 63 | | Bibliography |
| 64 | | References |
| 65 | Part Two | The General Theory of Relativity |
| 67 | 3 | The Principle of Equivalence |
| 67 | 3 | The Principle of Equivalence |
| 67 | 1 | Statement of the Principle |
| | | Equivalence of gravitation and inertia |
| | | Analogy with metric geometry |
| | | The weak and strong principles of equivalence |
| 70 | 2 | Gravitational Forces |
| | | The equation of motion |
| | | The affine connection |
| | | The metric tensor |
| | | Motion of photons |
| | | Light travel times |
| | | Determination of the locally inertial frames |
| 73 | 3 | Relation between gμν and Γλμν |
| | | Derivatives of the metric in terms of the affine connection |
| | | The Principle of Equivalence sharpened |
| | | Solution for the affine connection |
| | | Inverse of the metric tensor |
| | | Variational form of the equations of motion |
| | | Geodesics |
| 77 | 4 | The Newtonian Limit |
| | | Relation between g00 and the Newtonian potential |
| 79 | 5 | Time Dilation |
| | | Time dilation in a gravitational field |
| | | Red shift of spectral lines |
| | | The solar red shift |
| | | White dwarf red shifts |
| | | The Pound-Rebka experiment |
| | | Red and blue shifts from artificial satellites |
| | | Quantum derivation |
| 85 | 6 | Signs of the Times |
| | | Congruence relating the metric and Minkowski tensors |
| | | Sylvester's law of inertia |
| | | Signs of the metric eigenvalues |
| 86 | 7 | Relativity and Anisoptropy of Inertia |
| | | Mach versus Newton |
| | | The Einstein Compromise |
| | | The Hughes-drever experiment |
| 88 | | Bibliography |
| 89 | | References |
| 91 | 4 | Tensor Analysis |
| 91 | 4 | Tensor Analysis |
| 91 | 1 | The Principle of General Covariance |
| | | General covariance as an expression of the Principle of Equivalence |
| | | Contrast between general covariance and Lorentz invariance |
| | | Dynamics symmetries |
| | | General covariance sufficient only on small scales |
| 93 | 2 | Vectors and Tensors |
| | | Scalars, contravariant vectors, covariant vectors, tensors |
| | | The metric and the Kronecker tensors |
| | | Invariant equations |
| 96 | 3 | Tensor Algebra |
| | | Linear combinations |
| | | Direct products |
| | | Contraction |
| | | Raising and lowering indices |
| 98 | 4 | Tensor Densities |
| | | Transformation of the metric determinant |
| | | Scalar densities |
| | | Tensor densities |
| | | Weights |
| | | Volume elements as scalar densities |
| | | The Levi-Civita tensor density |
| | | Tensor density algebra |
| 100 | 5 | Transformation of the Affine Connection |
| | | The inhomogeneous transformation law |
| | | Transformation of derivatives of the metric tensor |
| | | Alternative derivation of the relation beetween the affine connection and metric tensor |
| | | alternative derivation of the equation of motion |
| 103 | 6 | Covariant Differentiation |
| | | Transformation of derivatives of tensors |
| | | Covariant derivatives of tensors |
| | | Covariant derivatives of tensor densities |
| | | Linear combinations, direct products, contraction |
| | | Covariant derivative of the metric tensor |
| | | Raising and lowering indices |
| | | Algorithm for the effects of gravitation |
| 106 | 7 | Gradient, Curl, and Divergence |
| | | Covariant derivatives of scalars |
| | | Antisymmetric covariant derivatives of vectors |
| | | Covariant divergence of vectors |
| | | Trace of the affine connection |
| | | Gauss's theorem |
| | | Cyclic sums of covariant derivatives |
| 108 | 8* | Vector Analysis in Orthogonal Coordinates |
| | | Diagonal metrics |
| | | “Ordinary” components |
| | | Volumes |
| | | Scalar products |
| | | Gradient, curl, and divergence |
| | | The Laplacian |
| 110 | 9 | Covariant Differentiation Along a Curve |
| | | Derivative along a curve |
| | | Vectors |
| | | Tensors |
| | | Relation to ordinary covariant derivatives |
| | | Parallel transport |
| 111 | 10* | The Elecctromagnetic Analogy |
| | | Gauge invariance |
| | | Gauge-covariant derivatives |
| | | Conserved currents |
| 121 | 5 | Effects of Gravitation |
| 131 | 6 | Curvature |
| 151 | 7 | Einstein's Field Equations |
| 173 | Part Three | Applications of General Relativity |
| 175 | 8 | Classic Tests of Einstein's Theory |
| 211 | 9 | Post-Newtonian Celestial Mechanics |
| 251 | 10 | Gravitational Radiation |
| 297 | 11 | STellar Equilibrium and Collapse |
| 355 | Part Four | Formal Developments |
| 357 | 12 | The action Principle |
| 375 | 13 | Symmetric Spaces |
| 405 | Part Five | Cosmology |
| 407 | 14 | Cosmography |
| 469 | 15 | Cosmology: the Standard Model |
| 635 | | Appendix |
| 641 | | Index |
| 657 | | _ |
| 658 | | ___ |
