Special Relativity in General Frames: From Particles to Astrophysics

Eric Gourgoulhon

Springer, 2013

784 pages

Special relativity is presented by adopting a four-dimensional point of view from the start. A distinctive feature of the book is that it doesn’t restrict itself to inertial frames and considers accelerated and rotating observers. It is thus possible to treat physical effects such as the Thomas precession or the Sagnac effect in a simple yet precise manner. In the final chapters, more advanced topics like tensorial fields in spacetime, exterior calculus, relativistic hydrodynamics and relativistic gravity are addressed. Illustrated by 178 figures and enriched by many historical notes, this book also presents many applications of special relativity, ranging from particle physics (accelerators, particle collisions, quark-gluon plasma) to astrophysics (relativistic jets, active galactic nuclei), and including practical applications (Sagnac gyrometers, synchrotron radiation, GPS). In addition, the book provides some mathematical developments, such as the detailed analysis of the Lorentz group and its Lie algebra.

Contents:

1. Minkowski Spacetime

2. Worldlines and Proper Time

3. Observers

4. Kinematics 1: Motion with Respect to an Observer

5. Kinematics 2: Change of Observer

6. Lorentz Group

7. Lorentz Group as a Lie Group

8. Inertial Observers and Poincaré Group

9. Energy and Momentum

10. Angular Momentum

11. Principle of Least Action

12. Accelerated Observers

13. Rotating Observers

14. Tensors and Alternate Forms

15. Fields on Spacetime

16. Integration in Spacetime

17. Electromagnetic Field

18. Maxwell Equations

19. Energy-Momentum Tensor

20. Energy-Momentum of the Electromagnetic Field

21. Relativistic Hydrodynamics

22. What about Relativistic Gravitation?

A. Basic Algebra

B. Web Pages

C. Special Relativity Books

More details on http://relativite.obspm.fr/sperel/