GRAVITATION

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.

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