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Summary
This landmark text offers a rigorous full-year graduate level course on gravitation physics, teaching students to: Grasp the laws of physics in flat spacetime Predict orders of magnitude Calculate using the principal tools of modern geometry Predict all levels of precision Understand Einstein's geometric framework for physics Explore applications, including pulsars and neutron stars, cosmology, the Schwarzschild geometry and gravitational collapse, and gravitational waves Probe experimental tests of Einstein's theory Tackle advanced topics such as superspace and quantum geometrodynamics The book offers a unique, alternating two-track pathway through the subject: In many chapters, material focusing on basic physical ideas is designated as Track 1. These sections together make an appropriate one-term advanced/graduate level course (mathematical prerequisites: vector analysis and simple partial-differential equations). The book is printed to make it easy for readers to identify these sections. The remainingTrack 2material provides a wealth of advanced topics instructors can draw from to flesh out a two-term course, with Track 1 sections serving as prerequisites.
Table of Contents
Gravitation has an innovative two-track organization. Within chapters, specific material designated "Track 1" covers the key physical ideas that make up the indispensable core of gravitation theory. The remaining material, designated "Track 2" covers advanced topics.
• = Chapters which include at least some Track 1 material
Part I. Spacetime Physics • 1. Geometrodynamics in Brief
Part II. Physics in Flat Spacetime • 2. Foundations of Special Relativity • 3. The Electromagnetic Field 4. Electromagnetism and Differential Forms • 5. Stress-Energy Tensor and Conservation Laws • 6. Accelerated Observers 7. Incompatibility of Gravity and Special Relativity
Part III. The Mathematics of Curved Spacetime • 8. Differential Geometry: An Overview 9. Differential Topology 10. Affine Geometry: Geodesics, Parallel Transport and Covariant Derivatives 11. Geodesic Deviation and Spacetime Curvature 12. Newtonian Gravity in the Language of Curved Spacetime 13. Riemannian Geometry: Metric as Foundation of All 14. Calculation of Curvature 15. Bianchi Identities and the Boundary of a Boundary
Part IV. Einstein's Geometric Theory of Gravity • 16. Equivalence Principle and Measuremetn of the "Gravitational Field" • 17. How Mass-Energy Generates Curvature • 18. Weak Gravitational Fields • 19. Mass and Angular Momentum of a Gravititing System 20. Conservation Laws for 4-Momentum and Angular Momentum 21. Variation Principle and Initial-Value Data 22. Thermodynamics, Hydrodynamics, Electrodynamics, Geometric Optics, and Kinetic Theory
Part V. Relativistic Stars • 23. Spherical Stars • 24. Pulsars and Neutron Stars: Quasars and Supermassive Stars • 25. The "Pit in the Potential" as the Central New Feature of Motion in Schwarzschild Geometry 26. Stellar Pulsations
Part VI. The Universe 27. Idealized Cosmologies • 28. Evolution of the Universe into Its Present State 29. Present State and Future Evolution of the Universe 30. Anisotropic and Inhomogeneous Cosmologies
Part VII. Gravitational Collapse and Black Holes • 31. Schwarzschild Geometry • 32. Gravitational Collapse • 33. Black Holes 34. Global Techniques, Horizons, and Singularity Theorems
Part VIII. Gravitational Waves • 35. Propagation of Gravitational Waves • 36. Generation of Gravitational Waves • 37. Detection of Gravitational Waves
Part IX. Experimental Tests of General Relativity • 38. Testing the Foundations of Relativity • 39. Other Theories of Gravity and the Post-Newtonian Approximation • 40. Solar-System Experiment
Part X. Frontiers 41. Spinors 42. Regge Calculus 43. Superspace: Arena for the Dynamics of Geometry 44. Beyond the End of Time