Blanchet L., Spallicci A., Whiting B. (Eds.) Mass and Motion in General Relativity

Подождите немного. Документ загружается.

Fundamental Theories of Physics

Volume 162

Series Editors

Philippe Blanchard, Universit¨at Bielefeld, Bielefeld, Germany

Paul Busch, University of York, Heslington, York, United Kingdom

Bob Coecke, Oxford University Computing Laboratory, Oxford, United Kingdom

Detlef Duerr, Mathematisches Institut, M¨unchen, Germany

Roman Frigg, London School of Economics and Political Science, London, United Kingdom

Christopher A. Fuchs, Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada

Giancarlo Ghirardi, Universit`a di Trieste, Trieste, Italy

Domenico Giulini, Leibnitz Universit¨at Hannover, Hannover, Germany

Gregg Jaeger, Boston University CGS, Boston, USA

Claus Kiefer, Universit¨at K¨oln, K¨oln, Germany

Klaas Landsman, Radboud Universiteit Nijmegen, Nijmegen, The Netherlands

Christian Maes, K.U. Leuven, Leuven, Belgium

Hermann Nicolai, Max-Planck-Institut f¨ur Gravitationsphysik, Golm, Germany

Vesselin Petkov, Concordia University, Montreal, Canada

Alwyn van der Merwe, University of Denver, Denver, USA

Rainer Verch, Universit¨at Leipzig, Leipzig, Germany

Reinhard Werner, Leibnitz Universit¨at Hannover, Hannover, Germany

Christian W¨uthrich, University of California, San Diego, La Jolla, USA

For further volumes:

http://www.springer.com/series/6001

Luc Blanchet  Alessandro Spallicci

Bernard Whiting

Editors

Mass and Motion

in General Relativity

ABC

Editors

Luc Blanchet

Institut d’Astrophysique de Paris

98 bis Boulevard Arago

75014 Paris

France

blanchet@iap.fr

Alessandro Spallicci

Universit´e d’Orl´eans

Observatoire des Sciences

de l’Univers en r´egion Centre

LPC2E-CNRS, 3A Avenue

de la Recherche Scientiﬁque

45071 Orl´eans

France

spallicci@cnrs-orleans.fr

Bernard Whiting

University of Florida

Department of Physics

P.O. Box 118440, Gainesville

FL 32611-8440, U.S.A.

bernard@phys.uﬂ.edu

ISBN 978-90-481-3014-6 e-ISBN 978-90-481-3015-3

DOI 10.1007/978-90-481-3015-3

Springer Dordrecht Heidelberg London New York

Library of Congress Control Number: 2010938712

 Springer Science+Business Media B.V. 2011

No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by

any means, electronic, mechanical, photocopying, microﬁlming, recording or otherwise, without written

permission from the Publisher, with the exception of any material supplied speciﬁcally for the purpose

of being entered and executed on a computer system, for exclusive use by the purchaser of the work.

Cover design: Spi Publisher Services

Printed on acid-free paper

Springer is part of Springer Science+Business Media (www.springer.com)

Mass and Motion in General Relativity



From the inﬁnitesimal scale of particle physics to the cosmic scale of the universe,

research is concerned with the nature of mass. While there have been spectacular

advances in physics during the past century, mass still remains a mysterious entity

at the forefront of current research. Particle accelerators in the quest for the Higgs

boson responsible for the mass of particles, laser interferometers that are sensitive

enough to respond to gravitational waves generated by the motion of astrophysi-

cal bodies, equivalence principle tests of the relationship between gravitational and

inertial mass are among the most ambitious and expensive experiments that funda-

mental physics has ever envisaged.

Our current perspective on gravitation has arisen over millennia, through falling

apples, lift thought experiments and stars spiraling into black holes. In this volume,

the world’s leading scientists offer a multifaceted approach to mass by giving a con-

cise and introductory presentation into their particular research on gravity. The main

theme is mass and its motion within general relativity and other theories of gravity,

particularly for compact bodies. Within this framework, all articles are tied together

coherently, covering post-Newtonian and related methods applied to in-spiraling

compact binaries, as well as the self-force approach to the analysis of motion.

All contributions reﬂect the fundamental role of mass in physics, from issues

related to Newton’s laws, via the effect of self-force and radiation reaction within

theories of gravitation, to the role of the Higgs boson in modern physics. Precision

measurements are described in detail; modiﬁed theories of gravity reproducing ex-

perimental data are investigated as alternatives to dark matter and the fundamental

problem of reconciling the theory of gravity with the physics of quantum ﬁelds is

addressed.

Radiation and motion have been hotly debated within general relativity from the

inception of the theory well beyond the theoretician’s arena. Mass and motion are

intimately intertwined as self-acceleration depends directly on the mass of the body



Lectures from the School on Mass held at Orl´eans on 23–25 June 2008

Organised by the Observatoire des Sciences de l’Univers en r´egion Centre OSUC, Universit´e

d’Orl´eans UO, Centre National de la Recherche Scientiﬁque CNRS

vi Mass and Motion in General Relativity

experiencing it. Recent developments have shown that the computation of radiation

reaction is unavoidable for determining the gravitational waveforms emitted not

only by large bodies in binary formation but also from sources such as the capture

of stellar size objects by super-massive black holes.

The main theme of this volume is indeed mass and its motion within general

relativity (and other theories of gravity), particularly for compact bodies, to which

many articles directly refer.

Within this framework, after a presentation of the mass and momentum in gen-

eral relativity (Jaramillo and Gourgoulhon), there are chapters on post-Newtonian

(Blanchet, Sch¨afer), effective one-body (Damour and Nagar) methods as well as on

the self-force approach to the analysis of motion (Wald with Gralla, Detweiler, Pois-

son, Barack, Gal’tsov). post-Newtonian and self-force methods converge in their

common domain of applicability (Blanchet, Detweiler, Le Tiec and Whiting). A

snapshot on the state of the art of the self-force (Burko) and the historic devel-

opment of the ﬁeld including future perspectives for the classic free fall problem

(Spallicci) conclude this central part.

Auxiliary chapters set the context for these theoretical contributions within a

wider context. The space mission LISA (Jennrich) has been designed to detect the

gravitational waves from EMRI captures. Motion in modern gravitation demands

an account of the relation between vacuum ﬂuctuations and inertia (Jaekel and

Reynaud). A volume centred on the fundamental role of mass in physics should face

issues related to the basic laws of mechanics proposed by Newton (L¨ammerzahl)

and precision measurements (Davis).

The role of the Higgs boson within physics is to give a mass to elementary parti-

cles (Djouadi), by interacting with all particles required to have a mass and thereby

experiencing inertia.

Motion of stars and of galaxies are explicable according to most researchers

by only evoking yet undetected matter and energy constituting around 95% of our

universe. A proposed alternative to dark matter theories is due to the modiﬁed theo-

ries of gravity (Esposito-Far`ese) such as MOND (MOdiﬁed Newtonian Dynamics).

Even if general relativity does not explain gravity, there still remains the fundamen-

tal problem of reconciling any theory of gravity with the physics of quantum ﬁelds

(Noui), itself so well veriﬁed experimentally.

The book is based upon the lectures of the School on Mass held in Orl´eans,

France, in June 2008. The school was funded by CNRS Centre National de

la Recherche Scientiﬁque,INSUInstitut National des Sciences de l’Univers,

UO Universit

ed’Orl

eans, R

egion Centre, Conseil R

egional du Loiret, Observa-

toire de Paris and was organised by OSUC Observatoire des Sciences de l’Univers

en r

egion Centre and its associated laboratory LPC2E Laboratoire de Physique et

Chimie de l’Environnement et de l’Espace.

The editors wish to thank the OSUC director (Elisabeth Verg`es) for continuous

support and organisation of the school; the OSUC staff (S. Bouquet, T. Cantalupo,

L. Catherine, N. Rolland) who dealt with all issues related to the practical or-

ganisation and running of two international events (the School followed up by

the 11th Capra meeting on radiation reaction); the LPC2E director (M. Tagger)

Mass and Motion in General Relativity vii

for suggestions and hosting the Capra workshop; the local CNRS delegation

(P. Letourneux) for assistance and support; M. Volkov (Univ. Tours) for suggestions

and all members of the scientiﬁc and organisation committees, especially S. Cordier

(MAPMO - Univ. Orl´eans).

Both events are shown on the OSUC web pages: http://www.cnrs-orleans.fr/osuc/

conf/

The contributions to this book have been anonymously refereed and revised by

the editors.

Luc Blanchet

Alessandro Spallicci

Bernard Whiting

Editors

Contents

Mass and Motion in General Relativity ......................................... v

The Higgs Mechanism and the Origin of Mass ................................. 1

Abdelhak Djouadi

1 The Standard Model and the Generation of Particle Masses ................ 1

1.1 The Elementary Particles and Their Interactions ..................... 2

1.2 The Standard Model of Particle Physics .............................. 3

1.3 The Higgs Mechanism for Mass Generation.......................... 5

2 The Proﬁle of the Higgs Particle .............................................. 8

2.1 Characteristics of the Higgs Boson.................................... 8

2.2 Constraints on the Higgs Boson Mass................................. 9

2.3 The Higgs Decay Modes and Their Rates............................. 11

3 Higgs Production at the LHC.................................................. 13

3.1 The Large Hadron Collider ............................................ 13

3.2 The Production of the Higgs Boson ................................... 14

3.3 Detection of the Higgs Boson ......................................... 15

3.4 Determination of the Higgs Boson Properties ........................ 18

4 The Higgs Beyond the Standard Model....................................... 20

5 Conclusions .................................................................... 22

References ........................................................................... 23

Testing Basic Laws of Gravitation – Are Our Postulates

on Dynamics and Gravitation Supported by Experimental

Evidence? ........................................................................... 25

Claus L¨ammerzahl

1 Introduction – Why Gravity Is So Exceptional ............................... 25

2 Key Features of Gravity ....................................................... 27

3 Standard Tests of the Foundations of Special and General Relativity ....... 28

3.1 Tests of Special Relativity ............................................. 28

3.2 Tests of the Universality of Free Fall .................................. 30

3.3 Tests of the Universality of the Gravitational Redshift ............... 31

3.4 The Consequence....................................................... 32