This book is an introduction to the theories of Special and General Relativity. The target audience are physicists, engineers and applied scientists who are looking for an understandable introduction to the topic - without too much new mathematics. The fundamental equations of Einstein's theory of Special and General Relativity are derived using matrix calculus, without the help of tensors. This feature makes the book special and a valuable tool for scientists and engineers with no experience in the field of tensor calculus. In part I the foundations of Special Relativity are developed, part II describes the structure and principle of General Relativity. Part III explains the Schwarzschild solution of spherical body gravity and examines the "Black Hole" phenomenon. Any necessary mathematical tools are user friendly provided, either directly in the text or in the appendices.

This book addresses physicists working in general relativity, astrophysics and cosmology. The contributions are based on reports given at a summer school the goal of which was to review modern research for students. The school was centered on the study of gravitational fields corresponding to rotating objects of astrophysical interest, under different viewpoints: theoretical, numerical and observational. Special emphasis is put on the analysis of interior and exterior fields of stationary axisymmetric systems. Lectures and contributions, collected here in Part I, ranged from basic information useful to newcomers to technical points pertaining to current research in this area. Part II contains lectures and contributions on other aspects of gravitation theory.

List of Participants **. **. *. . . . *. . **. . . **. **. *. *. . . **. *. *. . . **. * xi I. MOSS / The Quantum Origin of the Universe ****. *. *. ***. ***. *** M. S. TUru~ER / Cosmology and Particle Physics *. . ***. **. *. . ***. ** 19 G. GELMINI / Supersynunetry and the Early Universe ***. *. **. . *. *. . 115 J. D. BARROW / Relativistic Cosmology. . . . . . . . . . . . . . . . . . . . . . . . . . . 125 P. J. E. PEEBLES / Yet Another Scenario for Galaxy Formation . **. 203 ?:1. B. '-lISE / Non-Gaussian Fluctuations. . . . . . . . . . . . . . . . . . . . . . . . . . 215 S. D. H. mUTE / N-body Hethods and the Formation of Large-Scale Structure * . *. . . . * . * * . * * * . . . * . . . . * * . . . * . * . . 239 * . . . * * . . . . * T. PI~~ / Numerical Relativity and Cosmology. . . . . . . . . . . . . . . . . . . 261 J. R. BOND / Distortions and Anisotropies of the Cosmic Background Radiation *. *. . . **. **. ***. ****. . **. . *****. ** 283 J. V. HALL / The Early Universe - An Observer's View. . . . . . . . . . . . 335 G. GELHINI / Can the Solar Neutrino Problem be the First Detected Signature of Dark Hatter from the Halo of Our Galaxy? 351 A. K. DRUKIER / Detecting Cold Dark !1atter Candidates *. *. *. . . *. . 361 S. TOULMIN / The Early Universe: Historical and Philosophical Perspectives . *. *. . . . . . . *. . . . ***. *. *. *. *. . . . ****. . *. *. * 393 INDEX . . *. . . *. . . **. . . ****. . . *****. . . *. *. *. . *. . . . *. . *. *. . . **. ***.

Published in honour of Marc Feix this book tries to give a thorough overview of mathematical methods, analytical and numerical techniques and simulations applied to a variety of problems from physics and engineering. The book addresses graduate students, researchers and especially engineers. The main emphasis is to apply the generality of methods to form a coherent and stimulating approach to practical investigations.

The articles collected in this volume cover topics ranging from Planck-scale physics to galaxy clustering. They deal with various new ideas from cosmology, astrophysics and particle physics that might lead to a better understanding of our physical universe. Among the topics covered are inflationary models, nucleosynthesis, dark matter, large-scale clustering, cosmic microwave background radiations and more. The book addresses researchers but it also gives a good overview of the subject for graduate students in astrophysics and particle physics.

Black holes are one of the most remarkable predictions of Einstein's general relativity. In recent years, ideas in brane-world cosmology, string theory and gauge/gravity duality have motivated studies of black holes in more than four dimensions, with surprising results. In higher dimensions, black holes exist with exotic shapes and unusual dynamics. Edited by leading expert Gary Horowitz, this exciting book is the first devoted to this new field. The major discoveries are explained by the people who made them: Rob Myers describes the Myers-Perry solutions that represent rotating black holes in higher dimensions; Ruth Gregory describes the Gregory-Laflamme instability of black strings; and Juan Maldacena introduces gauge/gravity duality, the remarkable correspondence that relates a gravitational theory to nongravitational physics. Accessible to anyone with a standard course in general relativity, this is an important resource for graduate students and researchers in general relativity, string theory and high energy physics.

The observational evidence for the existence of black holes has grown significantly over recent decades. Stellar-mass black holes are detected as X-ray sources in binary systems, while supermassive black holes, with masses more than a million times the mass of the Sun, lurk in the nuclei of galaxies. These proceedings provide a useful and up-to-date overview of the observations of black holes in binaries, in the center of the Milky Way, and in the nuclei of galaxies, presented by leading expert astronomers. Special attention is given to the formation (including the recent evidence from gamma-ray bursts), physical properties, and demographics of black holes.

Indispensable for the building of cosmological models are precise observational data. To provide such data is the main purpose of this book. First, an analysis of recent cosmological observations using artificial satellites and large ground-based telescopes is given. Among these are the observation of the spatial distribution of galaxies and clusters, the detection of peculiar velocity fields in large regions, and the measurement of anisotropies in the microwave background radiation. Second, the authors present theoretical models which best fit the given observational data. The book addresses graduate students and astronomers and astrophysicists.

Supergravity can be seen as an intermediate step between general relativity and a future quantum theory of gravity. For the reader familiar with the basic concepts, this volume gives a concise presentation of both conformal and Poincare supergravity. The consistent four-dimensional supergravity theories are classified. For the practitioner in this field the book will be a valuable source, in particular with respect to the rather awkward formulae needed for further modelling, which have been carefully checked by the author. The book will be helpful not only for researchers, but also for advanced students."

The five lectures presented in this volume address very timely mathematical problems in relativity and cosmology. "Part I" is devoted to the initial value and evolution problems of the Einstein equations. Especially it deals with the Einstein-Yang-Mills-Boltzmann system, fluid models with finite or infinite conductivity, global evolution of a new (two-phase) model for gravitational collapse and the structure of maximal, asymptotically flat, vacuum solutions of the constraint equations which have the additional property of containing trapped surfaces. "Part II" focuses on geometrical-topological problems in relativity and cosmology: on the role of cosmic censorship for the global structure of the Einstein-Maxwell equations and on the mathematical structure of quantum conformal superspace.

This book gives a comprehensive overview of the current observational and theoretical status in the field of the local and general interstellar medium. It contains contributions presented at the IAU Colloquium No. 166. Review articles and highlight talks will serve both as an introduction to the field for the undergraduate or the non-specialist and also give a summary of the most recent developments for the expert and researcher. These articles are supplemented by a representative number of original research papers. All contributions are fully refereed and have been edited with extensive care to provide a high-standard reference book. The scientific content spans a wide range from solar system measurements of dust grains to X-ray emission from distant galaxies.

This book addresses graduate students in the first place and is meant as a modern compendium to the existing texts on black hole astrophysics. The authors present in pedagogically written articles our present knowledge on black holes covering mathematical models including numerical aspects and physics and astronomical observations as well. In addition, in their write-up of a panel discussion the participants of the school address the existence of black holes consenting that it has by now been verified with certainty.

Jean-Pierre Vigier continually labeled one of les heretiques de la science, l'eternel resistant et le patriarche is yet a pillar of modern physics and mathematics, with one leg firmly planted in theory and the other in empiricism spanning a career of nearly 60 years with a publication vitae quickly approaching 400! He wrote of his mentor Louis de Broglie "Great physicists fight great battles", which perhaps applies even more so to 1 Jean-Pierre Vigier himself . If fortune allows a visit to Paris, reported to be the city of love, and certainly one of the most beautiful and interesting cities in the world; one has been treated to a visual and cultural feast. For example a leisurely stroll from the Musee du Louvre along the Champs-Elysees to the Arc de Triomphe would instill even the least creative soul with the entelechies of a poets muse. It is perhaps open to theoretical interpretation, but if causal conditions have allowed one to be a physicist, visiting Paris, one may have taken opportunity to visit the portion of the old Latin quarter in place Jussieu where Pierre et Marie Curie Universite, reported to be 'the best university in France', is stationed.

1. The Workshop and this Tome In the excellent bucolic setting of SchloB Ringberg in Upper Bavaria, over 50 scientists assembled during the week of 23-28 September 1996 to discuss recent results, both theoretical and observational in nature, on the large scale structure of the Universe. Such a topic is perhaps nowadays far too encompassing, and is essentially all of what we used to call "observational cosmology. " The original philosophy of the organization of this meeting was deliber ated aimed at the younger community and their contributions. As a conse quence, the content of the presentations was refreshingly new, as it should be. In spite of the deficiences caused by the lack of certain key researchers in this field, for one reason or another, the final result was rewarding to all. Although the conference was held in Fall 1996, the contributions contained herein were submitted as late as Spring 1998, thus the content maintains some degree of trendiness. Originally the current volume was to be a "proceedings. " This refers to the usual archival tome that fills one's shelf and is rarely consulted, except to see the canonical group photo, which by the way, we also have. Nevertheless, I wanted something more than that. Although the field is rapidly changing, with so-called facts in a state ofconstant volubility, now is a good time for reflection prior to the commencement ofthe Sloan Survey, presumably the definitive large-scale program of low- to moderate-redshift galaxies in our lifetime.

This is an exhaustive review of our theoretical and observational knowledge of gravitational lensing 10 years after the discovery of the first lensed quasar, Q0957+561. Gravitational optics, optical, infrared, and radio observations of quasar-lens candidates, microlensing, arcs in clusters of galaxies, and radio rings are presented. In particular, the continuing survey of quasar-lens candidates, the new measurement of the time delay in 0957+561, the suspended microlensing effect through the galaxy 2237+030, as well as the discovery of new arcs and the measurement of new redshifts for two of them are presented. Numerous papers on the modelling of arcs and rings show how it should be possible to probe dark matter with these unexpected gravitational telescopes. Finally, tables summarize all the lens candidates we know today.

In the last few years modified gravity theories have been proposed as extensions of Einstein's theory of gravity. Their main motivation is to explain the latest cosmological and astrophysical data on dark energy and dark matter. The study of general relativity at small scales has already produced important results (cf e.g. LNP 863 Quantum Gravity and Quantum Cosmology) while its study at large scales is challenging because recent and upcoming observational results will provide important information on the validity of these modified theories. In this volume, various aspects of modified gravity at large scales will be discussed: high-curvature gravity theories; general scalar-tensor theories; Galileon theories and their cosmological applications; F(R) gravity theories; massive, new massive and topologically massive gravity; Chern-Simons modifications of general relativity (including holographic variants) and higher-spin gravity theories, to name but a few of the most important recent developments. Edited and authored by leading researchers in the field and cast into the form of a multi-author textbook at postgraduate level, this volume will be of benefit to all postgraduate students and newcomers from neighboring disciplines wishing to find a comprehensive guide for their future research.

This is the first volume in a series of books on the general theme of Supersymmetric Mechanics; the series is based on lectures and discussions held in 2005 and 2006 at the INFN-Laboratori Nazionali di Frascati. This volume supplies a pedagogical introduction, at the non-expert level, to the attractor mechanism in space-time singularities. After a qualitative overview, explicit examples realizing the attractor mechanism are treated at length.

This monograph presents in detail the reduction method for studying the unification of fundamental actions. The mathematical (differential geometrical) methods make extensive use of Lie Groups and the concept of homogeneous spaces. The main topic of the book is the dimensional reduction of pure Yang-Mills theories. A rather complete analysis of the structure of the scalar field potential is given and a general procedure for solving the equations of spontaneous compactification within Einstein-Yang-Mills systems is presented. The authors also discuss gravity and theories with fermions included and they review attempts to construct realistic models. The book presents the basic ideas and the calculations in detail and should be of interest to researchers and graduate students in mathematical physics.

Multiply charged ions have always been in the focus of atomic physics, astrophysics, plasma physics, and theoretical physics. Within the last few years, strong progress has been achieved in the development of ion sources, ion storage rings, ion traps, and methods to cool ions. As a consequence, nowadays, experiments with ensembles of multiply charged ions of brilliant quality are performed in many laboratories. The broad spectrum of the experiments demonstrates that these ions are an extremely versatile tool for investigations in pure and applied physics. It was the aim of this ASI to bring together scientists working in different fields of research with multiply charged ions in order to get an overview of the state of the art, to sound out possibilities for fruitful cooperations, and to discuss perspectives for the future. Accordingly, the programme of the ASI reached from established areas like QED calculations, weak interactions, x-ray astronomy, x-ray lasers, multi photon excitation, heavy-ion induced fusion, and ion-surface interactions up to the very recently opened areas like bound-beta decay, laser and x-ray spectroscopy, and spectrometry of ions in rings and traps, and the interaction of highly charged ions with biological cells. Impressive progress in nearly all of the fields could be reported during the meeting which is documented by the contributions to this volume. The theoretical understand ing of QED and correlation effects in few-electron heavy ions is rapidly developing."

This volume contains invited papers and contributions delivered at the International Conference on Hamiltonian Mechanics: Integrability and Chaotic Behaviour, held in Tornn, Poland during the summer of 1993. The conference was supported by the NATO Scientific and Environmental Affairs Division as an Advanced Research Workshop. In fact, it was the first scientific conference in all Eastern Europe supported by NATO. The meeting was expected to establish contacts between East and West experts as well as to study the current state of the art in the area of Hamiltonian Mechanics and its applications. I am sure that the informal atmosphere of the city of Torun, the birthplace of Nicolaus Copernicus, stimulated many valuable scientific exchanges. The first idea for this cnference was carried out by Prof Andrzej J. Maciejewski and myself, more than two years ago, during his visit in Greece. It was planned for about forty well-known scientists from East and West. At that time participation of a scientist from Eastern Europe in an Organising Committee of a NATO Conference was not allowed. But always there is the first time. Our plans for such a "small" conference, as a first attempt in the new European situation -the Europe without borders -quickly passed away. The names of our invited speakers, authorities in their field, were a magnet for many colleagues from all over the world.

The 1996 Carg se Summer Institute on Frontiers in Particle Physics was organized by the Universite Pierre et Marie Curie, Paris (M. Levy), the Ecole Nonnale SupCrieure, Paris (J. lliopoulos), the Katholieke Universiteit Leuven (R. Gastmans), and the Universite Catholique de Louvain (J.-M. Gerard), which, since 1975, have joined their efforts and worked in common. It was the twelfth Sunnner Institute on High Energy Physics organized jointly at Carg se by three of these universities. The Standard Model for fundamental interactions is constructed on two essential ingredients: the gauge symmetry and the mass generation mechanism. Now that the gauge theory aspect has been finnly established, the new challenge for the young researchers in elementary particle physics is the understanding of the origin of the masses. The standard Higgs mechanism is believed to be responsible for generating the masses of ALL fundamental particles. Professor D. Treille discussed the prospects for Higgs boson search and described the experimental determinations of the gauge boson masses. The influence of the top quark mass on electroweak processes has been emphasized by Professor J.L. Rosner, while Professor M. Neubert introduced the heavy-quark effective theory which allows you to get rid of heavy-quark masses. The theoretical determinations of the light quark masses have been critically analyzed by Professor H. Leutwyler. Professor A. Pich presented the various experimental tests on lepton universality and Professor R.L. MBssbauer reviewed our present knowledge on the neutrino masses."

Justbefore the preliminary programof Orbis Scientiae 1998 went to press the news in physics was suddenly dominated by the discovery that neutrinos are, after all, massive particles. This was predicted by some physicists including Dr. Behram Kusunoglu, who had apaper published on this subject in 1976 in the Physical Review. Massive neutrinos do not necessarily simplify the physics of elementary particles but they do give elementary particle physics a new direction. If the dark matter content ofthe universe turns out to consist ofneutrinos, the fact that they are massive should make an impact on cosmology. Some of the papers in this volume have attempted to provide answers to these questions. We have a long way to go before we find the real reasons for nature's creation of neutrinos. Another neutrino-related event was the passing of their discoverer, Fredrick Reines: The trustees of the Global Foundation, members of the Orbis Scientiae 1998, dedicate this conference to Fredrick Reines of the University of California at Irvine. The late Professor Reines was a loyal and active member of these series of conferences on the frontiers of physics and cosmology since 1964. He also sewed as one of the trustees of the Global Foundation for the past three years. Professor Reines discovered the most elusive particle, the neutrino, in 1954. We are proud to say that we recognized the importance of this discovery by awarding him the J.

The Symposium .Symmetries in Science VI: From the Rotation Group to Quantum Algebras. was held at the Cloister Mehrerau, Bregenz, Austria, during the period August 2-7, 1992. The Symposium was held in honor of Professor Lawrence C. Biedenharn on the occasion of his 70th birthday. During the academic year 1966/67 I worked as research associate with Larry at Duke University and we have ever since maintained close contact. It was thus natural for me to take the initiative and to organize this Symposium in honor of Larry as a great scientist and friend. The response which the Symposium received showed the favorable reaction by the scientific community to the opportunity provided by the Symposium to honor our colleague, teacher and friend. Equally, the scientific contributions contained in this volume illustrate the high esteem in which he is held. I wish to thank all the scientists who participated in the Symposium and who contributed to this volume. It is due to their commitment that the Symposium was successful. Finally I need to thank those who provided financial and logistical assistance to the Symposium: Dr. John H. Guyon, President of Southern Illinois University at Carbondale, Dr. Russell R. Dutcher, Dean, College of Science at SIUC, Dr. Maurice A. Wright, Chairman, Department of Physics, SIUC, Dr. Victoria J. Molfese, Office of Research Developement and Administration, SIUC, as well as Dr. Martin Purtscher, Landeshauptmann, Land Vorarlberg Dr. Guntram Lins, Landesrat, Land Vorarlberg."

The NATO Advanced Study Institute on The Nuclear Equatioo of State was held at Peiiiscola Spain from May 22- June 3, 1989. The school was devoted to the advances, theoretical and experimental, made during the past fifteen years in the physics of nuclear matter under extreme conditions, such as high compression and high temperature. Moie than 300 people had applied for participatio- this demonstrates the tremendous interest in the various subjects presented at the school. Indeed, the topic of this school, namely the Nuclear Equatioo of State, * plays the central role in high energy heavy ion collisions; * contains the intriguing possibilities of various phase transitions (gas - vapor, meson condensation, quark - gluon plasma); * plays an important role in the static and dynamical behavior of stars, especially in supernova explosions and in neutron star stability. The investigation on the nuclear equation of state can only be accomplished in the laboratory by compressing and heating up nuclear matter and the only mechanism known to date to achieve this goal is through shock compression and -heating in violent high energy heavy ion collisions. This key mechanism has been proposed and highly disputed in of high energy heavy ion physics, the early 70's. It plays a central role in the whole field and particularly in our discussions during the two weeks at Peiiiscola.