Gravitation

About this book

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 remaining Track 2 material provides a wealth of advanced topics instructors can draw from to flesh out a two-term course, with Track 1 sections serving as prerequisites.

Contents

• = 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

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