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Reference Frames
and
Gravitomagnetism
A. San Miguel and F. Vicente
World Scientific
Reference Frames
and
Gravitomagnetism
This page is intentionally left blank
Proceedings of the XXIII Spanish Relativity Meeting on
Reference Frames
and
Gravitomagnetism
Valladolid, Spain 6-9 September 2000
Editors
J. F. Pascual-Sanchez, L. Floria
A. San Miguel and F. Vicente
Universidad de Valladolid, Spain
V fe World Scientific
«k SSininagaappoorree • • N Neeww J Jeerrsseeyy ' L'Loonnddoonn • • Hong Kong
Published by
World Scientific Publishing Co. Pte. Ltd.
P O Box 128, Farrer Road, Singapore 912805
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British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
REFERENCE FRAMES AND GRAVITOMAGNETISM
Proceedings of the XXIII Spanish Relativity Meeting
Copyright © 2001 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
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ISBN 981-02-4631-5
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PREFACE
This is the 23rd occasion in which the Spanish Relativity Meeting — En-
cuentros Relativistas Esparioles (ERE)— has been held. This time (September,
6-9, 2000) Valladolid has acted as the host University and City for EREs2000.
Every year most of the Spanish scientific community developing active research
in the fields of Relativity, Gravitation and Cosmology every year gather in this
series of ERE Meetings, which are also attended by some of the leading inter
national specialists at the highest level. Due to these facts, the ERE Meetings
have been acquiring an unquestionable international prestige and scientific rep
utation, mainly during the last decade.
This year, the Scientific Programme has consisted of morning sessions
devoted to Invited Lectures dealing with the main subject(s): Reference
frames and Gravitomagnetism, and afternoon parallel sessions for Oral
Communications. One of the series of Communications was also dedicated to
the said topic of Reference frames and Gravitomagnetism. Consequently, we
hope that the present book will constitute a useful introduction to the current
state of the art in this field, since most of the volume concerns this topic and
an updated general list of references on this subject is also included.
A key point concerning Gravitomagnetism is that it shows the main differ
ence between Newton's theory of gravitation and the linear approximation of
Einstein's General Relativity, which would be something similar to what hap
pens with the difference between Coulomb's electricity and Maxwell-Lorentz's
electromagnetism. In this Proceedings, the various tools, both theoretical and
experimental, for testing this crucial difference, are discussed.
Within the wider framework of Gravitoelectromagnetism, the analogy be
tween the linear theory of Electromagnetism and linearized General Relativity
has been extended to the nonlinear regime by means of the introduction of an
observer formalism of nonlinear reference frames and it has provided the stimu
lus to develop a more complete and clear picture of the theoretical framework of
extending time-plus-space language and concepts to strong field gravity. Some
works along this line are also published in this book, including the implica
tions of the theory of relativistic reference frames for the GPS communication
system and Astrometry.
After more than thirty years, the gyroscope Gravity Probe B project
to measure the gravitomagnetic Lense-Thirring effect is nearing completion.
Meanwhile, indirect evidence has been reported concerning possible observa
tions and measurements of this effect by LAGEOS satellites orbiting the Earth.
v
VI Preface
The current state of these and other proposed gravitomagnetic experiments,
as the Gravity Probe Ci k, are also reviewed in this book.
oc
We would like to thank the Invited Speakers for accepting to deliver their
Lectures in the Meeting. We are also grateful to the participants, and specially
to those who accepted to act as the Chairperson of a scientific session. We
are in debt to the people who helped us to organize the Meeting, specially
F.J. Tapiador for the graphic implementation of the poster and the members
of the Organizing Committee, I. Aparicio (database support and web page)
and M. Esteban Pineiro. Also, we would like to express our gratitude to all
Institutions that provided some financial help. In particular we must mention:
the Spanish Ministerio de Ciencia y Tecnologia, the Junta de Castilla y Leon
regional government and the University of Valladolid.
The Organizing Committee wishes all the participants to have enjoyed a
stimulating and friendly atmosphere during the Meeting, in both scientific and
personal sense.
Finally, we wish to recall that, in the opening ceremony, we also had the
opportunity to pay homage to Professor Jose Martinez Salas for all his scien
tific and academic career.
Valladolid, January 2001 The editors
J.-F. Pascual-Sanchez
L. Floria
A. San Miguel
F. Vicente
CONTENTS
Preface v
INVITED LECTURES ON REFERENCE FRAMES AND GRAVITOMAGNETISM
Spacetime splitting techniques and gravitoelectromagnetism
in general relativity 1
D. Bini and R. T. Jantzen
Gravitoelectromagnetism: applications to black hole
circular orbits 13
D. Bini and R. T. Jantzen
Gravitomagnetism, Lense-Thirring effect and de Sitter
precession 25
/. Ciufolini
Gravitomagnetic phenomena due to spin, Lense-Thirring effect
and its 1995-2000 measurements with earth satellites 35
J. Ciufolini
Elements for a theory of relativistic coordinate systems.
Formal and physical aspects 53
B. Coll
Black hole astrophysics: Gravitomagnetism and
non keplerian orbits 67
F. de Felice
Theory of relativistic-reference frames for high-precision
astrometric space misions 79
S. M. Kopeikin
Geometry and dynamics of the brane-world 93
R. Maartens
Gravitoelectromagnetism 121
B. Mashhoon
Vll
Vlll Contents
Relativity and nonlocality 133
B. Mashhoon
General electric-magnetic decomposition of fields, positivity
and Rainich-like conditions 145
J. M. M. Senovilla
COMMUNICATIONS ON REFERENCE FRAMES AND GRAVITOMAGNETISM
The dominant energy condition and generalised
Rainich conditions 165
G. Bergqvist
On turning over gyroscopic precession 171
J. L. Herndndez-Pastora, J. Martin and E. Ruiz
Solid and ocean earth tides and the detection of some
gravitomagnetic effects 179
L. Iorio
Properties of Bel currents 185
R. Lazkoz, J. M. M. Senovilla and R. Vera
Sagnac and the g-clock effect revisited 191
A. Tartaglia
A List of references on spacetime splitting and
gravitoelectromagnetism 199
D. Bini and R. T. Jantzen
INVITED LECTURE* AND COMMUNICATIONS ON OTHER TOPICS
On thermal equilibrium in general relativity 227
E. Santos- Corchero*
Entropy in the universe: A new approach 237
A. Alfonso-Faus
On cyclically symmetrical spacetimes 241
A. Barnes
Contents ix
A theory of time-varying constants 247
J. A. Belinchon and A. Alfonso-Faus
Relations between lightlike foliations and observers
in symplectic mechanics 253
V. J. Bolos, V. Liern and J. Olivert
Scalar field cosmologies 259
J. Carot and M. M. Collinge
Thermodynamics and the dominant energy condition in
gravity theories 265
M. Cataldo and S. del Campo
Twisting type-N fields with symmetries 271
F. J. Chinea and F. Navarro-Lerida
Ideal gas Stephani universes 279
B. Coll and J. J. Ferrando
Constructing models for stars and voids in the universe:
A comprehensive approach 285
F. Fayos, J. M. M. Senovilla and R. Torres
Vacuum spacetimes with an isometry 293
F. Fayos and C. F. Sopuerta
Multipole corrections to perihelion and node line precession 299
L. Fernandez-Jambrina
Comments on purely electric Weyl tensors 305
J. J. Ferrando and J. A. Sdez
Ring-down of an accreting black hole 311
J. A. Font and P. Papadopoulos
Magnetised cosmological perturbations: A dynamical
systems approach 317
S. Hobbs and P. K. S. Dunsby
