Lecture Notes in Physics

Lecture Notes

in Physics

Edited by H. Araki, Kyoto, J. Ehlers, Menchen, K. Hepp, Zerich

R. Kippenhahn, Menchen, H. A. Weidenm~iller, Heidelberg

and J. Zittartz, K6ln

212

Gravitation,. Geometry

and RelatMstic Physics

Proceedings of the "Journ6es Relativistes"

Held at Aussois, France, May 2-5, 1984

Edited by Laboratoire "Gravitation et Cosmologie

Relativistes", Universit6 Pierre et Marie Curie et C.N.R.S.,

Institut Henri Poincar6, Paris

Springer-Verlag

Editor

Laboratoire de Physique Th~orique "Gravitation et C o s m o l o g i e Relativistes" C.N.R.S./U.A. 769~ Universit~ Pierre et Marie Curie, Institut Henri Poincar~ 11, rue Pierre et Marie Curie, F-75231 Paris Cedex 05, France

ISBN 3-540-13881-1 Springer-Verlag Berlin Heidelberg N e w York Tokyo ISBN 0-387-13881-1 Springer-Verlag N e w York Heidelberg Berlin Tokyo This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to =Verwertungsgesellschaft Wort", Munich.

© by Springer-Verlag Berlin Heidelberg 1984 Printed in Germany

Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr.

P R E F A C E

X

This year our laboratory has organized the "Journ~es R e l a t i v i s t e s " in Aussois ~ from May the 2nd to May the 5th and edited the following proceedings.

Twenty-five years ago the theoretical tools f o r r e l a t i v i s t i c g r a v i t a t i o n used to look very specialized and the orders of magnitude of the effects too small f o r experimentation. Then the f i e l d was often thought of as rather isolated. Nowadays t h i s opinion is no longer v a l i d .

Since the e a r l y days the subject has exploded in d i f f e r e n t directions and merged into several topics related to almost a l l the f i e l d s in physics. This results in a s c i e n t i f i c community which has no precise name but exists nevertheless. In t h i s community, the researchers are more or less specialized but the community i t s e l f is not : on one hand, sophisticated structures and geometrical tools are studied and used in mathematics and theoretical physics ; on the other hand, technological pro- gress and the paucity of deep empirical knowledge provide the experimentalists with a strong motivation whatever the d i f f i c u l t i e s are.

As the d i f f e r e n t possible topics cover a broad range of'preoccupations, we chose to emphasize the physical points of view : theoretical and experimental physics, astrophysics and cosmology. Within t h i s framework, the key words of the meeting were "synthesis" and "prospect".

As a synthesis our goal was i ) to present the developments of the subject from the e a r l y Riemannian geometry u n t i l nowadays with physical, epistemological and h i s t o r i c a l points of view : geometry, general r e l a t i v i t y , experimental g r a v i t a t i o n . . .

Laboratoire de Physique Th~orique, "Gravitation et Cosmologie R e l a t i v i s t e s " , C.N.R.S./U.A. 769, Universit~ Pierre et Marie Curie, I n s t i t u t Henri Poincar~, 11 rue Pierre et Marie Curie - 75231 Paris Cedex 05.

IV

i i ) to summarize the s i t u a t i o n of several impor- tant subjects concerning r e l a t i v i s t i c g r a v i t a t i o n and related topics : thermal back- ground r a d i a t i o n , g r a v i t a t i o n a l lenses, i n f l a t i o n a r y universe . . .

As prospects we chose to emphasize i ) the d i v e r s i t y and the v i t a l i t y of "geometrical physics", including r e l a t i v i s t i c g r a v i t a t i o n and r e l a t i v i t y : general r e l a t i v i t y , supergravity, atomic physics, s o l i d state physics . . .

i i ) the necessity of extra theoretical studies and c l a r i f i c a t i o n s in several f i e l d s where experiments and observations dis- play a high accuracy : geodesy, atomic physics . . .

i i i ) the f r u i t f u l n e s s of experimental g r a v i t a t i o n (and e s p e c i a l l y of g r a v i t a t i o n a l wave detection experiments) which was the s t a r t i n g point of recent discussions and works on quantum non-demolition t , squeezed states, addition of laser f i e l d s , high performance interferometers . . .

I f conclusions were to be drawn from the meeting, on one hand I would put forward that besides the t r a d i t i o n a l problems (e.g. quantum g r a v i t y , g r a v i t a t i o n a l f i e l d s from given sources, e a r l y universes . . . ) there exists an expanding f i e l d of preoccupations in "geometrical physics" related to very d i f f e r e n t t h e o r e t i c a l , obser- vational and experimental topics. On the other hand, I would e s p e c i a l l y emphasize that several precise theoretical questions, o r i g i n a t i n g from the increasing accuracy of experiments and observations, have been asked during t h i s meeting. They provide theoreticians with subjects f o r r e f l e c t i o n and require answers in the near f u t u r e .

We a l l especially acknowledge F. A l l i x and C. Trecul f o r t h e i r material organization of the meeting and C. Trecul f o r her help in the elaboration of the following proceedings.

September 1984

Ph. TOURRENC

Directeur du laboratoire

I ABLE OF CONTENTS

I, GENERAL RELATIVITY

page J.N. GOLDBERG. Developments and Predictions . . . 1 Lo BLANCHET. Radiative G r a v i t a t i o n a l Fields and Radiation Reaction Forces in General R e l a t i v i t y . . . 18 J. MARTIN, E. RUIZ and M.J. SENOSIAIN. Multipoles P a r t i c l e s in General

R e l a t i v i t y : the Weyl and Kerr Metrics . . . 29 J. KIJOWSKI. Unconstrained Degrees of Freedom of G r a v i t a t i o n a l F i e l d and

the P o s i t i v i t y of G r a v i t a t i o n a l Energy . . . 40 J. HAJJ-BOUTROS. A Method f o r Generating Exact Solutions of E i n s t e i n ' s

F i e l d Equations . . . 51 C. BARRABES. Causal R e l a t i v i s t i c Thermodynamics of T r a n s i t o r y Processes in Electromagnetic Continuous Media . . . 54 Jo EISENSTAEDT. La r e l a t i v i t 6 g~n~rale : une th~orie sans probl6me(s) ? .. 57

I I

A. LICHNEROWICZ. G~om#trie et Physique . . . 77 Y. CHOQUET-BRUHAT. Supergravities . . . 88 HU HESHENG (H.S. HU). Some Nonexistence Theorems f o r Massive Vang-Mills

Fields and Harmonic Maps . . . 107 D.M.L.F. SANTOS. Geometrical Approach to the Physics of Random Networks .. 117 J.B. KAMMERER. The Algebra of M u l t i p l i c a t i o n Operators of Star-Product

in R 2n . . . 129 D. CANARUTTO and C.T.J. DODSON. Manifold b-lncompleteness S t a b i l i t y Via

a Structure of Principal Connections . . . 132 X. JAEN, A. MOLINA and J. LLOSA. Front Form P r e d i c t i v e R e l a t i v i s t i c

Mechanics Non I n t e r a c t i o n Theorem . . . 134 J. CARMINATI and R.G. MC LENAGHAN. Some New Results on the V a l i d i t y of

Vl

page

III,EXPERIMENTAL RELATIVITY AND GRAVITATION

P. TEYSSANDIER. Theories of Gravity and Experimental Tests in the

Post-Newtonian L i m i t . . . 154

C. BOUCHER and J.F. LESTRADE. Survey of R e l a t i v i s t i c Effects in Geodesy and Fundamental Astronomy . . . 174

J.P. BRIAND. R e l a t i v i s t i c Effects in Heavy Ions . . . 187

A. BRILLET. The I n t e r f e r o m e t r i c Detection of Gravitational Waves . . . 195

J. HOUGH, S. HOGGAN, G.A. KERR, J.B. MANGAN, B.J. NEERS, G.P. NEWTON, N.A. ROBERTSON, H. WARD and R.W.P. DREVER. The Development of Long Baseline Gravitational Radiation Detectors a t Glasgow University . . . 204

R. SCHILLING, L. SCHNUPP, D.H. SHOEMAKER, W. WINKLER, K. MAISCHBERGER and A. RODIGER. Improved S e n s i t i v i t i e s in Laser Interferometers f o r the Detection of Gravitational Waves . . . 213

C.N. MAN and A. BRILLET. I n j e c t i o n Locking and Coherent Summation of Argon Ion Lasers . . . ~ .. . . 222

A. HEIDMANN and S. REYNAUD. Can the Photon Noise Be Reduced ? . . . . . 226

N. DERUELLE and Ph. TOURRENC. The Problem of the Optical S t a b i l i t y of a Pendular Fabry-Perot . . . 232

IV,

R. FABBRI. The 3K Background Radiation : Observational and Theoretical Status . . . 249

C. VANDERRIEST. Close-up on Gravitational Lensing : the Gravitational Mirages . . . 265

F. HAMMER. A m p l i f i c a t i o n o f Light by Gravitational Lens : Dynamics and Thick Lens Effects . . . 281

D. PAVON and J.M. RUBI. Thermodynamical Fluctuations of Massive Black Holes . . . 286

B. BARBERIS and D. GALLETTO. Newtonian and R e l a t i v i s t i c Bianchi I Models o f the Universe . . . 290

A. BLANCHARD and F.X. DESERT. The Cosmological Constant . . . 294

R. HAKIM. The I n f l a t i o n a r y Universe : a Primer . . . 302