New book: “Special Relativity in General Frames” by Eric Gourgoulhon

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.

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

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New book: “The General Theory of Relativity: A Mathematical Exposition” by Anadijiban Das and Andrew DeBenedictis

Anadijiban Das and Andrew DeBenedictis
“The General Theory of Relativity: A Mathematical Exposition”
705 pages, 105 figures.
Springer (2012).

“The General Theory of Relativity: A Mathematical Exposition” will serve readers as a modern mathematical introduction to the general theory of relativity. Throughout the book, examples, worked-out problems, and exercises (with hints and solutions) are furnished. Topics in this book include, but are not limited to:

– tensor analysis,
– the special theory of relativity,
– the general theory of relativity and Einstein’s field equations,
– spherically symmetric solutions and experimental confirmations,
– static and stationary space-time domains,
– black holes,
– cosmological models,
– algebraic classifications and the Newman-Penrose equations,
– the coupled Einstein-Maxwell-Klein-Gordon equations,
– appendices covering mathematical supplements and special topics,

Mathematical rigor, yet very clear presentation of the topics make this book a unique text for both university students and research scholars.

For full publication details please see:

New book: “3+1 Formalism in General Relativity” by Eric Gourgoulhon

3+1 Formalism in General Relativity: Bases of Numerical Relativity

Eric Gourgoulhon
Springer, 2012
294 pages

1. Introduction
2. Basic Differential Geometry
3. Geometry of Hypersurfaces
4. Geometry of Foliations
5. 3+1 Decomposition of Einstein Equation
6. 3+1 Equations for Matter and Electromagnetic Field
7. Conformal Decomposition
8. Asymptotic Flatness and Global Quantities
9. The Initial Data Problem
10. Choice of Foliation and Spatial Coordinates
11. Evolution Schemes
A. Conformal Killing Operator and Conformal Vector Laplacian
B. Sage Codes

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Free access to all papers published in “Gravitation and Cosmology”

Free full text versions of all papers published in the international journal “Gravitation and Cosmology” (Grav. Cosmol.) during 1995-2007 are now at the site of the Russian Gravitational Society (or Click “welcome”, then “Gravitation and Cosmology”, then “old issues”, then issue (volume, number), then title of the paper, then in the last line “here”.

As from 2008 the journal “Gravitation and Cosmology” is distributed by Springer, contents of all issues and abstracts of papers published in 2008-2009 in the journal may be found at the site:

All other info and subscription details are at the site:
Please, recommend the subscription to this journal of your institute or university library for 2010.

Best regards,
Prof. Vitaly Melnikov,