General relativity ranks among the most accurately tested fundamental theories in all of physics. Deficiencies in mathematical and conceptual understanding still exist, hampering further progress. This book collects surveys by experts in mathematical relativity writing about the current status of, and problems in, their fields. There are four contributions for each of the following mathematical areas: differential geometry and differential topology, analytical methods and differential equations, and numerical methods.

For this set of lectures we assumed that the reader has a reasonable back ground in physics and some knowledge of general relativity, the modern theory of gravity in macrophysics, and cosmology. Computer methods are present ed by leading experts in the three main domains: in numerics, in computer algebra, and in visualization. The idea was that each of these subdisciplines is introduced by an extended set of main lectures and that each is conceived as being of comparable 'importance. Therefpre we believe that the book represents a good introduction into scientific I computing for any student who wants to specialize in relativity, gravitation, and/or astrophysics. We took great care to select lecturers who teach in a comprehensible way and who are, at the same time, at the research front of their respective field. In numerics we had the privilege of having a lecturer from the National Center for Supercomputing Applications (NCSA, Champaign, IL, USA) and some from other leading institutions of the world; visualization was taught by a visualization expert from Boeing; and in com puter algebra we took recourse to practitioners of different computer algebra systems as applied to classical general relativity up to quantum gravity and differential geometry.

This 2004 textbook fills a gap in the literature on general relativity by providing the advanced student with practical tools for the computation of many physically interesting quantities. The context is provided by the mathematical theory of black holes, one of the most elegant, successful, and relevant applications of general relativity. Among the topics discussed are congruencies of timelike and null geodesics, the embedding of spacelike, timelike and null hypersurfaces in spacetime, and the Lagrangian and Hamiltonian formulations of general relativity. Although the book is self-contained, it is not meant to serve as an introduction to general relativity. Instead, it is meant to help the reader acquire advanced skills and become a competent researcher in relativity and gravitational physics. The primary readership consists of graduate students in gravitational physics. It will also be a useful reference for more seasoned researchers working in this field.

This excellent textbook offers a unique take on relativity theory, setting it in its historical context. Ideal for those interested in relativity and the history of physics, the book contains a complete account of special relativity that begins with the historical analysis of the reasons that led to a change in our view of space and time. Its aim is to foster a deep understanding of relativistic spacetime and its consequences for Dynamics.

Here it is, in a nutshell: the history of one genius 's most crucial work discoveries that were to change the face of modern physics. In the early 1900s, Albert Einstein formulated two theories that would forever change the landscape of physics: the Special Theory of Relativity and the General Theory of Relativity. Respected American academic Professor Tai Chow tells us the story of these discoveries. He details the basic ideas of Einstein, including his law of gravitation. Deftly employing his inimitable writing style, he goes on to explain the physics behind black holes, weaving into his account an explanation of the structure of the universe and the science of cosmology.

Based on class-tested notes, this text offers an introduction to Conformal Field Theory with a special emphasis on computational techniques of relevance for String Theory. It introduces Conformal Field Theory at a basic level, Kac-Moody algebras, one-loop partition functions, Superconformal Field Theories, Gepner Models and Boundary Conformal Field Theory. Eventually, the concept of orientifold constructions is explained in detail for the example of the bosonic string. In providing many detailed CFT calculations, this book is ideal for students and scientists intending to become acquainted with CFT techniques relevant for string theory but also for students and non-specialists from related fields.

In 1919 the Prussian Ministry of Science, Arts and Culture opened a dossier on "Einstein's Theory of Relativity." It was rediscovered by the author in 1961 and is used in conjunction with numerous other subsequently identified 'Einstein' files as the basis of this fascinating book. In particular, the author carefully scrutinizes Einstein's FBI file from 1950-55 against mostly unpublished material from European including Soviet sources and presents hitherto unknown documentation on Einstein's alleged contacts with the German Communist Party and the Comintern. Siegfried Grundmann's thorough study of Einstein's participation on a committee of the League of Nations, based on archival research in Geneva, is also new.

This book outlines Einstein's image in politics and German science policy. It covers the period from his appointment as a researcher in Berlin to his fight abroad against the "boycott of German science" after World War I and his struggle at home against attacks on "Jewish physics" of which he was made a prime target. An important gap in the literature on Einstein is thus filled, contributing much new material toward a better understanding of Einstein's so rigorous break with Germany.

Stephen Webb, author of WHERE IS EVERYBODY?, takes the interested amateur on a thrilling and enlightening tour of the amazing, even bizarre, new ideas of modern physics, including alternatives to the Big Bang, parallel universes, and an imaginary trip to the other side of the black hole.

The theory, observations, and applications ofgravitational lensingconstitute one ofthe most rapidly growing branches ofextragalactic astrophysics. The deflection of light from very distant sources by intervening masses provides a unique possibility for the investigation of both background sources and lens mass distributions. Gravitational lensing manifestsitselfmost distinctly through multiply imaged QSOs and the formation of highly elongated im ages of distant galaxies ('arcs') and spectacular ring-like images of extra galactic radio sources. But the effects of gravitational light deflection are not limited to these prominent image configurations; more subtle, since not directly observable, consequences of lensing are the, possibly strong, mag nification of sources, which may permit observation of intrinsically fainter, or more distant, sources than would be visible without these natural tele scopes. Such light deflection can also affect the source counts of QSOs and of other compact extragalactic sources, and can lead to flux variability of sources owing to propagation effects. Trying to summarizethe theory and observationalstatus ofgravitational lensing in a monograph turned out to be a bigger problem than any of the authors anticipated when we started this project at the end of 1987, encour aged by Martin Harwit, who originally approached us. The development in the field has been very rapid during the last four years, both through the ory and through observation, and many sections have been rewritten several times, as the previous versions became out of date.

The scalar-tensor theory of gravitation is one of the most popular alternatives to Einstein's theory of gravitation. This book provides a clear and concise introduction to the theoretical ideas and developments, exploring scalar fields and placing them in context with a discussion of Brans-Dicke theory. Topics covered include the cosmological constant problem, time variability of coupling constants, higher dimensional space-time, branes and conformal transformations. The authors emphasize the physical applications of the scalar-tensor theory and thus provide a pedagogical overview of the subject, keeping more mathematically detailed sections for the appendices. This book is suitable for graduate courses in cosmology, gravitation and relativity. It will also provide a valuable reference for researchers.

Like a river, the progress of science has a tendency to run tast or slow. Once the water meets a dam, it may stop for a while, but eventually it will flow over the top and run fast again. In scientific research, a breakthrough to overcome a simile>r barrier is often made by a small number of scientists, or perhaps by a single person of special creativity, extraordinary talent and unusual perseverance. Through such individuals science can proceed in great strides. No one can deny that Professor Kazuo Takayanagi is one of these special individuals who have played a leading role in the field of atomic and molecular physics, as well as space physics. This book is dedicated to Professor Takayanagi on the occasion of his retirement from the Institute of Space and Astronautical Science. Professor Takayanagi was born in 1926 and grew up in Tomakomai in Hokkaido, the northern island of Japan. In his boyhood, he was interested in natural sciences, particularly astronomy. On 5th February, 1943, when he was attending secondary school, a solar eclipse was seen in his town. He organized a group of students from his school to observe the eclipse. He still remembers the scene: it grew so dark during the eclipse that two stars, Vega and Arcturus, could be seen. After graduation from the University of Tokyo in 1948, he entered the graduate school there.

The second Erice course in the school of Particle-Astrophysics was held in May, 1988. The topic choosen was Dark Matter. This is one of the most exciting top ics at the interface of particle physics and astrophysics. It is developing rapidly now due to a coming together not only of the theoretical concepts from the early universe with the theoretical concepts of galaxy formation, but also the coming to gether of the theorists, experimentalists and observers. It is with Dark Matter, the combined interrelated topics of galaxy formation and the generation of large scale structure that we see a confrontation of the exotic ideas from the early universe, such as phase transitions and unification, coming face to face with the realities of traditional observational cosmology. These realities have recently been heightened by the tremendous number of new observations, demonstrating that large scale structure of the universe is far more complex than anybody had suspected. In particular, we now see large scale foam, apparent large scale velocity fields, indicating devations from the Hubble flow, large scales of the order 100 Mpc, and galaxy formation occurring at high red shifts much greater than unity. We also see an apparent correlation of clusters of galaxies that may even exceed the c- relation of galaxies despite their being on much larger scales with lower average densities."

This monograph presents a self contained mathematical treatment of the initial value problem for shock wave solutions of the Einstein equations in General Relativity. It has a clearly outlined goal: proving a certain local existence theorem. Concluding remarks are added and commentary is provided throughout. The author is a well regarded expert in this area.

This is a book about physics, written for mathematicians. The readers we have in mind can be roughly described as those who: I. are mathematics graduate students with some knowledge of global differential geometry 2. have had the equivalent of freshman physics, and find popular accounts of astrophysics and cosmology interesting 3. appreciate mathematical elarity, but are willing to accept physical motiva tions for the mathematics in place of mathematical ones 4. are willing to spend time and effort mastering certain technical details, such as those in Section 1. 1. Each book disappoints so me readers. This one will disappoint: 1. physicists who want to use this book as a first course on differential geometry 2. mathematicians who think Lorentzian manifolds are wholly similar to Riemannian ones, or that, given a sufficiently good mathematical back ground, the essentials of a subject !ike cosmology can be learned without so me hard work on boring detaiis 3. those who believe vague philosophical arguments have more than historical and heuristic significance, that general relativity should somehow be "proved," or that axiomatization of this subject is useful 4. those who want an encyclopedic treatment (the books by Hawking-Ellis [1], Penrose [1], Weinberg [1], and Misner-Thorne-Wheeler [I] go further into the subject than we do; see also the survey article, Sachs-Wu [1]). 5. mathematicians who want to learn quantum physics or unified fieId theory (unfortunateIy, quantum physics texts all seem either to be for physicists, or merely concerned with formaI mathematics).

The accretion process is thought to play a key role in the Universe. This book explains, in a form intelligible to graduate students, its relation to the formation of new stars, to the energy release in compact objects and to the formation of black holes. The monograph describes how accretion processes are related to the presence of jets in stellar objects and active galactic nuclei and to jet formation. The authors treat theoretical work as well as current observational facts. This volume of the highly esteemed Les Houches series is meant as an advanced text that can serve to attract students to exciting new research work in astrophysics.

This volume consists of papers developed from a joint ACE/ISSI symposium at the occasion of the eightieth birthday of Johannes Geiss. The symposium explored insights into the composition of solar-system and galactic matter that have been brought about by recent space missions, ground-based studies, and theoretical advances. Coverage includes linking primordial to solar composition, planetary samples, solar sources and fractionation processes, and interstellar gas and Cosmic rays.

Modern cosmology is a quickly developing ?eld of research. New technical devices and tools supply the community with new experimental data measured with high accuracy. The self-consistent explanation of these data needs t- oretical models that are based on hypothetical predictions of particle theory. In their turn, such predictions imply cosmology for their probe. Speci?c st- ies of the cosmological consequences of particle theory, linking them to their observable signatures, are actual. This boiling kettle of theoretical research and experimental efforts produces ideas that will be preserved for following generations. The aim of this book is to acquaint the reader with some of these ideas, - fering nontrivial ways to probe the physical basis of modern cosmology. An extensive review of the newest ideas in modern cosmology, e. g. , related with the development of the M-brane theory, lies beyond the scope of our book, which is aimed at providing a ?rmly established system of probes for these ideas, linking their predictions to their possible experimental test. We use the framework of in?ationary paradigm to reveal the phenomena that can shed light on the physical origin of the observed Universe, of its matter content and large-scale structure. The crucial role of quantum ?uctuations in creation of our Universe and in possible features, re?ecting cosmological impact of microphysics, is discussed. These features are shown to be accessible to - perimental test in the near future.

REFLECTIONS ON SPACETIME - FOUNDATIONS, PHILOSOPHY AND HISTORY During the academic year 1992/93, an interdisciplinary research group constituted itself at the Zentrum fUr interdisziplinare Forschung (ZiF) in Bielefeld, Germany, under the title 'Semantical Aspects of Spacetime Theories', in which philosophers and physicists worked on topics in the interpretation and history of relativity theory. The present issue consists of contributions resulting from material presented and discussed in the group during the course of that year. The scope of the papers ranges from rather specialised issues arising from general relativity such as the problem of referential indeterminacy, to foundational questions regarding spacetime in the work of Carnap, Weyl and Hilbert. It is well known that the General Theory of Relativity (GTR) admits spacetime models which are 'exotic' in the sense that observers could travel into their own past. This poses a number of problems for the physical interpretation of GTR which are also relevant in the philosophy of spacetime. It is not enough to exclude these exotic models simply by stating that we live in a non-exotic universe, because it might be possible to "operate time machines" by actively changing the topology of the future part of spacetime. In his contribution, Earman first reviews the attempts of physicists to prove "chronology protection theorems" (CPTs) which exclude the operation of time machines under reasonable assumptions.

Sponsored by the Global Foundation, Inc., these proceedings are derived from the International Conference on Orbis Scientiae II. Topics covered include: gravitational mass, neutrino mass, particle masses, cosmological masses, susy masses, and big bang creation of mass.

This volume contains papers presented at an international conference to celebrate Fred Hoyle's monumental contributions to astronomy, astrophysics and astrobiology and more generally to humanity and culture. The contributed articles highlight the important aspects of his scientific life and show how much of an example and inspiration he has been for over three generations in the 20th century.
There are a few people of whom it could be said they changed the way we perceive the world. Galileo Galilei, Nicholas Copernicus and Isaac Newton were amongst these. The inclusion of Fred Hoyle in this elite group may be contentious at the moment for the reason that in challenging the most cherished of Holy Grails in science he unwittingly offended many. But once the dust has settled over the many disputes that were raised and in the fullness of time there can be little doubt that Fred Hoyle will be ranked alongside these figures of history.
Hoyle perceived science with an indomitable passion and an obsessive desire to find the truth wherever it lay. His singleness of purpose in this great mission and his deep suspicion of orthodoxy, his powerful intellect and imagination set him apart from most of his contemporaries in the last century.
This volume includes papers presented at a commemorative conference held in Cardiff in June 2002. The material divides naturally into several sections: Personal Reminiscences, Stellar Structure and Evolution, Cosmology, Interstellar Matter, Comets and finally Panspermia. Each article pays its own tribute to Fred Hoyle for his inspiration and guidance that led to major breakthroughs in astrophysics and space science throughout the 20th century.

Causal relations, and with them the underlying null cone or conformal structure, form a basic ingredient in all general analytical studies of asymptotically flat space-time. The present book reviews these aspects from the analytical, geometrical and numerical points of view. Care has been taken to present the material in a way that will also be accessible to postgraduate students and nonspecialist reseachers from related fields.

This book is written for theoretical and mathematical physicists and mat- maticians interested in recent developments in complex general relativity and their application to classical and quantum gravity. Calculations are presented by paying attention to those details normally omitted in research papers, for pedagogical r- sons. Familiarity with fibre-bundle theory is certainly helpful, but in many cases I only rely on two-spinor calculus and conformally invariant concepts in gravitational physics. The key concepts the book is devoted to are complex manifolds, spinor techniques, conformal gravity, ?-planes, ?-surfaces, Penrose transform, complex 3 1 - - space-time models with non-vanishing torsion, spin- fields and spin- potentials. 2 2 Problems have been inserted at the end, to help the reader to check his und- standing of these topics. Thus, I can find at least four reasons for writing yet another book on spinor and twistor methods in general relativity: (i) to write a textbook useful to - ginning graduate students and research workers, where two-component spinor c- culus is the unifying mathematical language.

Soliton theory is an important branch of applied mathematics and mathematical physics. An active and productive field of research, it has important applications in fluid mechanics, nonlinear optics, classical and quantum fields theories etc. This book presents a broad view of soliton theory. It gives an expository survey of the most basic ideas and methods, such as physical background, inverse scattering, Backl nd transformations, finite-dimensional completely integrable systems, symmetry, Kac-moody algebra, solitons and differential geometry, numerical analysis for nonlinear waves, and gravitational solitons. Besides the essential points of the theory, several applications are sketched and some recent developments, partly by the authors and their collaborators, are presented.

The Joint European and National Astronomical Meeting (JENAM) of 2002, was held in Porto - Portugal (2-7 September 2002), corresponding to the I ph Meeting of the European Astronomical Society (EAS) and the IJ! En- contra Nacional de Astronomia e Astroftsica (12ENAA) of the Sociedade Portuguesa de Astronomia (SPA). Portugal has a small and young community of researchers in Astronomy. This meeting have had an important role in marking the beginning of what we expect to be a new phase for Astronomy in Portugal. The fact that we have chosen to address '"the future" reflects this will of the Portuguese com- munity to share and discuss our commitment for the next decades with our colleagues. The meeting, titled "The Unsolved Universe: Challenges for the Fu- ture", aimed at discussing some of the major research programmes and objec- tives for the next decades. The scientific programme included the plenary ses- sions (invited reviews and highlight talks), whose contributions are published in this book, and several workshops on more specific topics.

This book is a comprehensive reference on differential geometry. It shows that Maxwell, Dirac and Einstein fields, which were originally considered objects of a very different mathematical nature, have representatives as objects of the same mathematical nature. The book also analyzes some foundational issues of relativistic field theories. All calculation procedures are illustrated by many exercises that are solved in detail.