General Relativity and Gravitational Waves
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Concise introduction by a pioneer in the investigation of gravitational waves explains the related Riemannian geometry and tensor calculus, conservation laws, and classic experiments. 1961 edition.
1The Equivalence Principle1.1The Eotvos Experiment11.2Negative Mass51.3Equivalence of Different Frames of Reference61.4Gravitational Red Shift of Spectral Lines81.5Further Remarks on the Equivalence Principle92Generalization of the Special Theory of Relativity2.1The Idea of Covariance112.2The Metric Tensor122.3The Metric Tensor in Curved Spaces and Accelerated Frames122.4General Covariance153Riemannian Geometry and Tensor Calculus3.1Some Ideas about Curvature173.2Transformation Laws for Different Kinds of Tensors183.3Parallel Displacement and Covariant Differentiation223.4The Curvature Tensor283.5The Bianchi Identities323.6Geodesics343.7Some Useful Calculational Aids373.8Length Measurements393.9Determination of the Metric Tensor414Field Equations of General Relativity and Electromagnetism4.1The Gravitational Field Equations434.2Variational Principle Deduction of the Field Equations504.3Maxwell's Equations534.4Motion of a Charged Particle545Experimental Tests of General Relativity5.1The Schwarzschild Solution565.2The Gravitational Red Shift605.3Effects on Planetary Orbits645.4Deflection of Light675.5Concluding Remarks696The Conservation Laws6.1The Canonical Stress Energy Pseudotensor706.2Other Conservation Laws796.3Further Remarks on the Conservation Laws857Gravitational Waves7.1Weak-Field Solutions877.2Riemann Tensor for a Wave of Arbitrary Strength Which is Locally Plane907.3Approximate Evaluation of Source Volume Integrals927.4Weak-Field Approximations for Energy Flux and Energy Density947.5Linear Mass Quadrupole Oscillator957.6Radiation from a Spinning Rod977.7Further Remarks on the Weak-Field Solutions987.8Exact Cylindrical Wave Solutions997.9Interaction of a Particle with Cylindrical Gravitational Waves1027.10Exact Plane-Wave Solutions1057.11Initial-Value Formulation of the Radiation Problem1077.12Time-Symmetric Solution With Positive Energy1107.13Conditions on the Differentiability and Continuity of Manifolds1137.14Six-Dimensional Treatment of Gravitational Radiation1137.15Other Petrov Class II Wave Solutions1198Detection and Generation of Gravitational Waves8.1Detection1248.2Mass Quadrupole Detector1268.3Interaction of a Crystal with a Gravitational Wave1318.4Rotations Induced by Gravitational Radiation1388.5Generation of Gravitational Waves1408.6Other Radiation Experiments1449Selected Topics in General Relativity9.1Unified Field Theories1469.2Equations of Motion1539.3Mach's Principle1579.4Remarks on Cosmology1629.5Hamiltonian Formulation1679.6Remarks on Quantization of General Relativity1849.7Spinors in General Relativity186Exercises191Index194
