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Graduate Texts in Physics

Éric Gourgoulhon

Relativity in
General Frames
From Particles to Astrophysics

Graduate Texts in Physics

For further volumes:

Graduate Texts in Physics
Graduate Texts in Physics publishes core learning/teaching material for graduate- and
advanced-level undergraduate courses on topics of current and emerging fields within
physics, both pure and applied. These textbooks serve students at the MS- or PhD-level and
their instructors as comprehensive sources of principles, definitions, derivations, experiments
and applications (as relevant) for their mastery and teaching, respectively. International
in scope and relevance, the textbooks correspond to course syllabi sufficiently to serve
as required reading. Their didactic style, comprehensiveness and coverage of fundamental
material also make them suitable as introductions or references for scientists entering, or
requiring timely knowledge of, a research field.

Series Editors
Professor William T. Rhodes
Department of Computer and Electrical Engineering and Computer Science
Imaging Science and Technology Center
Florida Atlantic University
777 Glades Road SE, Room 456
Boca Raton, FL 33431

Professor H. Eugene Stanley
Center for Polymer Studies Department of Physics
Boston University
590 Commonwealth Avenue, Room 204B
Boston, MA 02215

Professor Richard Needs
Cavendish Laboratory
JJ Thomson Avenue
Cambridge CB3 0HE

´ Gourgoulhon

Special Relativity
in General Frames
From Particles to Astrophysics


´ Gourgoulhon
Laboratoire Univers et Th´eories
Observatoire de Paris, CNRS, Universit´e Paris Diderot
Meudon, France

Translation from the French language edition of: Relativit´e restreinte: Des particules a`
c 2010 EDP Sciences, CNRS Edition, France.
ISSN 1868-4513
ISSN 1868-4521 (electronic)
Graduate Texts in Physics
ISBN 978-3-642-37275-9
ISBN 978-3-642-37276-6 (eBook)
DOI 10.1007/978-3-642-37276-6
Springer Heidelberg New York Dordrecht London
Library of Congress Control Number: 2013942463
c Springer-Verlag Berlin Heidelberg 2013

This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of
the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,
broadcasting, reproduction on microfilms or in any other physical way, and transmission or information
storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology
now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection
with reviews or scholarly analysis or material supplied specifically for the purpose of being entered
and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of
this publication or parts thereof is permitted only under the provisions of the Copyright Law of the
Publisher’s location, in its current version, and permission for use must always be obtained from Springer.
Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations
are liable to prosecution under the respective Copyright Law.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication
does not imply, even in the absence of a specific statement, that such names are exempt from the relevant
protective laws and regulations and therefore free for general use.
While the advice and information in this book are believed to be true and accurate at the date of
publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for
any errors or omissions that may be made. The publisher makes no warranty, express or implied, with
respect to the material contained herein.
Printed on acid-free paper
Springer is part of Springer Science+Business Media (www.springer.com)

To Val´erie and Maxime


The theory of special relativity holds a distinctive place within physics. Rather
than being a specific physical theory, it is (similar to thermodynamics or analytical
mechanics) a general theoretical framework within which various dynamical theories can be formulated. In this respect, a modern presentation of special relativity
must put forward its essential structures before illustrating them by concrete
applications to specific dynamical problems. Such is the challenge (so successfully
´ Gourgoulhon.
met!) of the beautiful book by Eric
Contrary to most textbooks on special relativity, which mix the presentation
of this theory with that of its historical development and which sometimes write
the specific form of “Lorentz transformations” before indicating that they leave a
´ Gourgoulhon is centred, from the
certain quadratic form invariant, the book by Eric
very beginning, on the essential structure of the theory, i.e. the chrono-geometric
structure of the four-dimensional Poincar´e–Minkowski spacetime. The aim is to
train the reader to formulate any relativity question in terms of four-dimensional
geometry. The word geometry has here the meaning of “synthetic geometry” (`a
la Euclid) in contrast with “analytic geometry” (`a la Descartes). Under the expert
´ Gourgoulhon, the reader will learn to set, and to solve, any problem
guidance of Eric
of relativity by drawing spacetime diagrams, made of curves, straight lines, planes,
hyperplanes, cones and vectors. He will get accustomed to visualizing the motion
of a particle as a line in spacetime, to think about the twin paradox as an application
of the “spacetime triangle inequality”, to express the local frame of an observer as
a four-dimensional generalization of the Serret–Frenet triad, to compute a spatial
distance as a geometric mean of time intervals (via the hyperbolic generalization of
the power of a point with respect to a circle) or to understand the Sagnac effect by
considering two helices in spacetime wound in opposite directions.
Besides the pedagogical characteristic of being centred on a geometric formu´
lation, the book by Eric
Gourgoulhon is remarkable in many other ways. First
of all, it is fully up to date and very complete in its coverage of the notions and
results where special relativity plays an important role: from Thomas precession to
the foundations of general relativity, including tensor calculus, exterior differential
calculus, classical electrodynamics, the general notion of energy–momentum tensor



and a noteworthy chapter on relativistic hydrodynamics. In addition, this book is
sprinkled with enlightening historical notes, in which the author summarizes in
a condensed, albeit very informative way the (sometimes very recent) results by
historians of science. Finally, the book is richly laden with many examples of
applications of special relativity to concrete physical problems. The reader will
learn the role of special relativity in various domains of modern astrophysics
(supernova nebulae, relativistic jets, micro-quasars) in the description of the quarkgluon plasma produced in heavy ion collisions, as well as in many high-technology
experiments: from laser gyrometers to the LHC, including modern replications of
the Michelson–Morley experiment, matter wave interferometers, synchrotrons and
their radiation, and the comparison of atomic clocks embarked on planes, satellites
or the International Space Station.
´ Gourgoulhon will attract the keen
I am sure that the remarkably rich book by Eric
interest of many readers and will enable them to understand and master one of the
fundamental pillars (with general relativity and quantum theory) of modern physics.
Bures-sur-Yvette, France

Thibault Damour

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