This volume studies spacetime structure, relativistic physics, and gravitation.
This volume studies spacetime structure, relativistic physics, and gravitation. It develops both special and general relativity with geometric and analytical methods.
Part I. Special Relativity
Chapter 1. Space and Time
1.1 Inertial frames 1.2 Galilean transformations 1.3 Postulates of relativity 1.4 Spacetime viewpoint 1.5 Examples
Chapter 2. Lorentz Transformations
2.1 Derivation 2.2 Time dilation 2.3 Length contraction 2.4 Velocity addition 2.5 Examples
Chapter 3. Relativistic Mechanics
3.1 Four-vectors 3.2 Energy and momentum 3.3 Mass-energy equivalence 3.4 Applications 3.5 Examples
Part II. Minkowski Spacetime
Chapter 4. Geometry of Spacetime
4.1 Minkowski metric 4.2 Light cones 4.3 Causal structure 4.4 Proper time 4.5 Examples
Chapter 5. Tensor Formulation
5.1 Tensor notation 5.2 Index manipulation 5.3 Invariant quantities 5.4 Applications 5.5 Examples
Chapter 6. Electromagnetism in Relativity
6.1 Field tensor 6.2 Covariant Maxwell equations 6.3 Lorentz invariance 6.4 Applications 6.5 Examples
Part III. General Relativity
Chapter 7. Curved Spacetime
7.1 Equivalence principle 7.2 Metric tensor 7.3 Geodesics 7.4 Examples 7.5 Applications
Chapter 8. Einstein Field Equations
8.1 Derivation (overview) 8.2 Stress-energy tensor 8.3 Solutions 8.4 Applications 8.5 Examples
Chapter 9. Classical Solutions
9.1 Schwarzschild solution 9.2 Black holes 9.3 Cosmological models 9.4 Applications 9.5 Examples
Part IV. Geometric Methods
Chapter 10. Differential Geometry Tools
10.1 Connections 10.2 Curvature tensors 10.3 Parallel transport 10.4 Applications 10.5 Examples
Chapter 11. Geodesic Motion
11.1 Free fall 11.2 Orbital motion 11.3 Light rays 11.4 Applications 11.5 Examples
Chapter 12. Global Structure
12.1 Singularities 12.2 Horizons 12.3 Causal diagrams 12.4 Applications 12.5 Examples
Part V. Relativistic Physics
Chapter 13. Relativistic Fluids
13.1 Energy-momentum tensor 13.2 Conservation laws 13.3 Applications 13.4 Examples 13.5 Connections
Chapter 14. Gravitational Waves
14.1 Linearized equations 14.2 Wave solutions 14.3 Detection 14.4 Applications 14.5 Examples
Chapter 15. Cosmology
15.1 Expanding universe 15.2 Friedmann equations 15.3 Dark matter and energy 15.4 Applications 15.5 Examples
Part VI. Advanced Topics
Chapter 16. Black Hole Physics
16.1 Event horizons 16.2 Thermodynamics of black holes 16.3 Hawking radiation (overview) 16.4 Applications 16.5 Examples
Chapter 17. Quantum Fields in Curved Spacetime
17.1 Particle creation 17.2 Vacuum states 17.3 Applications 17.4 Examples 17.5 Connections
Chapter 18. Alternative Theories of Gravity
18.1 Modified gravity models 18.2 Scalar-tensor theories 18.3 Applications 18.4 Examples 18.5 Connections
Part VII. Applications
Chapter 19. Astrophysics
19.1 Stellar structure 19.2 Compact objects 19.3 Observational tests 19.4 Applications 19.5 Examples
Chapter 20. Experimental Tests
20.1 Light bending 20.2 Time dilation experiments 20.3 Gravitational wave detection 20.4 Applications 20.5 Examples
Chapter 21. Computational Relativity
21.1 Numerical methods 21.2 Simulation of spacetime 21.3 Visualization 21.4 Applications 21.5 Examples
Part VIII. Research Directions
Chapter 22. Advanced Topics
22.1 Quantum gravity (overview) 22.2 String theory links 22.3 Loop quantum gravity overview 22.4 Modern developments 22.5 Emerging areas
Chapter 23. Open Problems
23.1 Unification with quantum theory 23.2 Singularities and horizons 23.3 Dark energy models 23.4 Computational challenges 23.5 Future directions
Chapter 24. Historical and Conceptual Notes
24.1 Development of relativity 24.2 Key contributors 24.3 Evolution of gravitational theory 24.4 Cross-disciplinary impact 24.5 Summary
Appendix
A. Tensor identities B. Metric examples C. Proof techniques checklist D. Numerical relativity methods E. Cross-reference to other MSC branches