Mathematics and General Relativity Proceedings of a Summer Research Conference held June 22-2831 1986 AMERICAn MATHEMATICAL SOCIETY VOLUME 71 http://dx.doi.org/10.1090/conm/071 Titles in This Series Volume 1 Markov random fields and their 20 Low dimensional topology, Samuel J. applications, Ross Kindermann and Lomonaco, Jr., Editor J. Laurie Snell 21 Topological methods In nonlinear 2 Proceedings of the conference on functional analysis. S. P. Singh, Integration, topology, and geometry S. Thomeier, and B. Watson, Editors In linear spaces. William H. Graves. 22 Factorizations of b" ± 1. b = Editor 2. 3, 5, 6, 7,10,11,12 up to high 3 The closed graph and P-closed powers. John Brillhart. D. H. Lehmer. graph properties In general topology, J. L. Selfridge, Bryant Tuckerman. and T. R. Hamlett and L. L. Herrington S. S. Wagstaff. Jr. 4 Problems of elastic stability and 23 Chapter 9 of Ramanujan's second vibrations. Vadim Komkov. Editor notebook-Infinite series Identities, 5 Rational constructions of modules for transformations, and evaluations. simple Lie algebras, George B. Seligman Bruce C. Berndt and Padmini T. Joshi 6 Umbral calculus and Hopf algebras. 24 Central extensions. Galois groups, Robert Morris, Editor and Ideal class groups of number fields, A. Frohlich 7 Complex contour Integral representation of cardinal spline 25 Value distribution theory and Its functions, Walter Schempp applications, Chung-Chun Yang, Editor 8 Ordered fields and real algebraic 26 Conference In modern analysis and geometry, D. W. Dubois and T. Recio, probability, Richard Beals. Anatole Beck. Editors Alexandra Bellow. and Arshag Hajian, Editors 9 Papers In algebra, analysis and statistics, R. Lidl, Editor 27 Mlcrolocal analysis. M. Salah Baouendi, Richard Beals, and Linda Preiss Rothschild, 10 Operator algebras and K-theory, Editors Ronald G. Douglas and Claude Schochet, Editors 28 Fluids and plasmas: geometry and dynamics, Jerrold E. Marsden. Editor 11 Plane ellipticity and related problems, Robert P. Gilbert, Editor 29 Automated theorem proving, 12 Symposium on algebraic topology In W. W. Bledsoe and Donald Loveland, Editors honor of Jos~ Adem, Samuel Gitler. Editor 30 Mathematical applications of 13 Algebraists' homage: Papers In category theory, J. W. Gray, Editor ring theory and related topics. 31 Axiomatic set theory, James E. S. A. Amitsur, D. J. Saltman, and Baumgartner, Donald A. Martin, and G. B. Seligman. Editors Saharan Shelah, Editors 14 Lectures on Nielsen fixed point 32 Proceedings of the conference on theory, Boju Jiang Banach algebras and several complex 15 Advanced analytic number theory. variables, F. Greenleaf and D. Gulick, Part 1: Ramification theoretic Editors methods. Carlos J. Moreno 33 Contributions to group theory, 16 Complex representations of Kenneth I. Appel, John G. Ratcliffe, and GL(2, K) for finite fields K, Paul E. Schupp, Editors llya Piatetski-Shapiro 34 Comblnatorlcs and algebra, 17 Nonlinear partial differential Curtis Greene. Editor equations. Joel A. Smaller, Editor 35 Four-manifold theory, Cameron Gordon 18 Fixed points and nonexpanslve and Robion Kirby, Editors mappings, Robert C. Sine. Editor 36 Group actions on manifolds, 19 Proceedings of the Northwestern Reinhard Schultz, Editor homotopy theory conference, 37 Conference on algebraic topology In Haynes R. Miller and Stewart B. Priddy, honor of Peter Hilton, Renzo Piccinini Editors and Denis Sjerve, Editors Titles in This Series Volume 38 Topics In complex analysis, Eric M. Friedlander. and Michael R. Stein. Dorothy Browne Shaffer. Editor Editors 39 Errett Bishop: Reflections on him 56 Multlparameter bifurcation theory, and his research, Murray Rosenblatt. Martin Golubitsky and John Guckenheimer. Editor Editors 40 Integral bases for affine Lie algebras 57 Comblnatorlcs and ordered sets, and their universal enveloping Ivan Rival. Editor algebras. David Mitzman 58.1 The Lefschetz centennial conference. 41 Particle systems. random media and Part 1: Proceedings on algebraic large deviations, Richard Durrett. Editor geometry, D. Sundararaman. Editor 58.11 The Lefschetz centennial conference. 42 Classical real analysis. Daniel Part II: Proceedings on algebraic Waterman. Editor topology, S. Gitler. Editor 43 Group actions on rings, Susan 58.111 The Lefschetz centennial Montgomery, Editor conference. Part Ill: Proceedings on 44 Combinatorial methods In topology differential equations. A. Verjovsky, and algebraic geometry, John R. Harper Editor and Richard Mandelbaum. Editors 59 Function estimates. J. S. Marron. 45 Finite groups-coming of age, Editor John McKay, Editor 60 Nonstrlctly hyperbolic conservation 46 Structure of the standard modules laws. Barbara Lee Keyfitz and for the affine Lie algebra ApJ. Herbert C. Kranzer. Editors James Lepowsky and Mirko Prime 61 Residues and traces of differential 47 Linear algebra and Its role In forms via Hochschlld homology, systems theory, Richard A. Brualdi, Joseph Lipman David H. Carlson. Biswa Nath Datta. 62 Operator algebras and mathematical Charles R. Johnson. and Robert J. physics, Palle E. T. Jorgensen and Plemmons. Editors Paul S. Muhly, Editors 48 Analytic functions of one complex 63 Integral geometry, Robert L. Bryant, variable, Chung-chun Yang and Victor Guillemin. Sigurdur Helgason. and Chi-tai Chuang, Editors R. 0. Wells. Jr .. Editors 49 Complex differential geometry and 64 The legacy of Sonya Kovalevskaya, nonlinear differential equations. Linda Keen, Editor Yum- Tong Siu. Editor 65 Logic and comblnatorlcs, Stephen G. 50 Random matrices and their Simpson. Editor applications. Joel E. Cohen, Harry 66 Free group rings, Narian Gupta Kesten. and Charles M. Newman. Editors 67 Current trends In arithmetical 51 Nonlinear problems In geometry, algebraic geometry, Kenneth A. Ribet, Dennis M. DeTurck, Editor Editor 52 Geometry of normed linear spaces, 68 Differential geometry: The R. G. Bartle. N. T. Peck. A. L. Peressini. Interface between pure and and J. J. Uhl, Editors applied mathematics, Mladen Luksic. Clyde Martin, and William Shadwick, 53 The Selberg trace formula and Editors related topics. Dennis A. Hejhal. 69 Methods and applications of Peter Sarnak. and Audrey Anne Terras, mathematical logic, Walter A. Carnielli Editors and Luiz Paulo de Alcantara. Editors 54 Differential analysis and Infinite 70 Index theory of elliptic operators. dimensional spaces. Kondagunta foliations, and operator algebras. Sundaresan and Srinivasa Swaminathan. Jerome Kaminker. Kenneth C. Millett. and Editors Claude Schochet. Editors 55 Applications of algebraic K-theory 71 Mathematics and general relativity, to algebraic geometry and number James A. Isenberg, Editor theory, Spencer J. Bloch. R. Keith Dennis. COnTEMPORARY IYIATHEIYIATICS Volume71 Mathematics and General Relativity Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference held June 22-28ll 1986 with support from the National Science Foundation James A. Isenberg, Editor AMERICAn MATHEMATICAL SOCIETY Providence • RhOda Island EDITORIAL BOARD Irwin Kra. managing editor M. Salah Baouendi William H. Jaco Daniel M. Burns Gerald J. Janusz David Eisenbud Jan Mycielski Jonathan Goodman The AMS-IMS-SIAM Joint Summer Research Conference in the Mathematical Sciences on Mathematics in General Relativity was held at the University of California, Santa Cruz on June 22-28, 1986, with support from the National Science Foundation. Grant DMS-8415201. 1980 Mathematics Subject Classification. {1985 Revision). Primary 83C. 35J, 35K, 35L, 538, 53C. 32-XX. Library of Congress Cataloging-In-Publication Data AMS-IMS-SIAM Joint Summer Research Conference in the Mathematical Sciences on Mathematics in General Relativity <1986 : University of California, Santa Cruz> Mathematics and general relativity : proceedings of the AMS-IMS -SIAM jOint summer research conference held June 22-28,1966 with support from the National Science Foundation I James A. Isenberg, editor. p. em. -- <Contemporary mathematics, ISSN 0271-4132 ; v. 71l Includes bibliographies. ISBN 0-8218-5079-2 1. General relativity <Physicsl--Mathematics--Congresses. 2. Mathematical physics--Congresses. I. Isenberg, James A. I I. Tit 1e. II I. Se r i e s . QC173.6.A47 1966 530.1'1--dc19 88-9685 CIP Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them. are permitted to make fair use of the material, such as to copy an article for use in teaching or research. 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