Spinor and Twistor Methods in Space-Time Geometry introduces the theory of twistors, and studies in detail how the theory of twistors and 2-spinors can be applied to the study of space-time. Twistors have, in recent years, attracted increasing attention as a mathematical tool and as a means of gaining new insights into the structure of physical laws. This volume also includes a comprehensive treatment of the conformal approach to space-time infinity with results on general-relativistic mass and angular momentum, a detailed spinorial classification of the full space-time curvature tensor, and an account of the geometry of null geodesics.

Based on courses taught at the University of Dublin, Carnegie Mellon University, and mostly at Simon Fraser University, this book presents the special theory of relativity from a mathematical point of view. It begins with the axioms of the Minkowski vector space and the flat spacetime manifold. Then it discusses the kinematics of special relativity in terms of Lorentz tranformations, and treats the group structure of Lorentz transformations. Extending the discussion to spinors, the author shows how a unimodular mapping of spinor (vector) space can induce a proper, orthochronous Lorentz mapping on the Minkowski vector space. The second part begins with a discussion of relativistic particle mechanics from both the Lagrangian and Hamiltonian points of view. The book then turns to the relativistic (classical) field theory, including a proof of Noether's theorem and discussions of the Klein-Gordon, electromagnetic, Dirac, and non-abelian gauge fields. The final chapter deals with recent work on classical fields in an eight-dimensional covariant phase space.

Man kann ohne Obertreibung sagen, daE es die Astronomie seit tiber fUnftausend J ahren als exakte Wissenschaft gibt. In dieser ganzen Zeit beriihrte sie die letzten Fragen der Mensch- heit. Ihre Geschichte niederzuschreiben stellt uns vor zahlIose Probleme. Wir beginnen mit einer Zeit, die wir weitgehend durch Schlu&folgerungen kennen; wir gehen dann zu Zeiten tiber, von denen wir wissen, da& das meiste Indizienmaterial verlorengegangen ist; und wir enden bei den letzten Dekaden eines Jahrhunderts, das den Astronomen Beachtung und wirtschaftliche Mittel in nie dagewesenem Umfang beschert hat. Aus einem typischen Jahrhundert der hellenistischen Ara, einem goldenen Zeitalter der Astronomie, mogen wir eine Handvoll Texte haben. 1m Gegensatz dazu werden heute jedes Jahr mehr als zwanzig- tausend astronomische Artikel veroffentlicht, und, tiber fUnfJahre genommen, ist die Zahl der Astronomen, unter deren Namen diese erscheinen, von der Ordnung vierzigtausend. Wenn diese Geschichte also am Anfang wie eine Skizze anmutet, ist sie notwendiger- weise am Schlu& eine Silhouette, die den Gegenstand ebenso durch das definiert, was sie ausla&t, als dadurch, was sie enthalt. Sie schreitet in einem solchen Ma& immer schneller voran, daE der Raum, der einem Dutzend hochstwichtiger neuer Bticher gewidmet wird, ein kleiner Bruchteil davon ist, was am Anfang einer heute ganz trivial erscheinenden Aussage eingeraumt wird. Das ist kein Zufall.

From H.G. Wells to Star Trek, audiences have been captivated by the notions of time travel, time warps, space warps, and wornholes. But science fiction is not the only realm where these concepts thrive. An active group of general relativists and quantum field theorists has produced a considerable body of serious (thought admittedly speculative) mathematical and physical analyses of the wormhole system. Now, with this fascinating book, readers can explore in depth the science behind the science fiction. Drawing on pivotal work by Einstein, Wheeler, Morris, Thorne, Hawking, and others, Matt Visser charts the development and current state of Lorentzian wormhole physics. Dr. Visser shows that by pushing established physical theories to their limits, it is possible to deduce the physical properties of such exotica as wormholes and time travel. The physical framework he uses is derived from one of the major research frontiers of modern theoretical physics: quantum gravity-the intersection of classical Einstein gravity and quantum field theory. Physicists, students of general relativity, cosmology, quantum physics, or any interested reader with a background in physics wil find this a provocative introduction to an exciting and active topic of ongoing research.

Reprint of a classical book first published in 1950. This lucid and profound exposition of Einstein's 1915 theory of gravitation is essential reading.

EDWIN TURNER AND RACHEL WEBSTER Co-Chairs, Scientific Organizing Committee lAU Symposium 173, Astrophysical Applications of Gravitational Lenses, was held in Melbourne, Australia from July 9-14, 1995. The Symposium was sponsored by lAU Commissions 47 and 40. With the discovery by Walsh and collaborators of the first instance of a gravitational lens, the multiply imaged quasar 0957+561, the area of grav itational lensing moved from speculative theory to a major astrophysical tool. Since that time, there have been regular, approximately biennial in ternational meetings both in Europe and in North America, which have specifically focussed on gravitational lensing. On this occasion, with the blessing of the lA U, the meeting was held at the University of Melbourne in Australia. It was the first international astronomical meeting to be held at the University of Melbourne, and hope fully has given the astronomical community some enthusiasm for trekking half-way round the globe to Australia to discuss their latest work.

A comprehensive review of gravitational effects in quantum field theory. Treatment is general, but special emphasis is given to the Hawking black hole evaporation effect and to particle creation processes in the early universe.

An authoritative interdisciplinary account of the historic discovery of gravitational waves In 1915, Albert Einstein predicted the existence of gravitational waves-ripples in the fabric of spacetime caused by the movement of large masses-as part of the theory of general relativity. A century later, researchers with the Laser Interferometer Gravitational-Wave Observatory (LIGO) confirmed Einstein's prediction, detecting gravitational waves generated by the collision of two black holes. Shedding new light on the hundred-year history of this momentous achievement, Einstein Was Right brings together essays by two of the physicists who won the Nobel Prize for their instrumental roles in the discovery, along with contributions by leading scholars who offer unparalleled insights into one of the most significant scientific breakthroughs of our time. This illuminating book features an introduction by Tilman Sauer and invaluable firsthand perspectives on the history and significance of the LIGO consortium by physicists Barry Barish and Kip Thorne. Theoretical physicist Alessandra Buonanno discusses the new possibilities opened by gravitational wave astronomy, and sociologist of science Harry Collins and historians of science Diana Kormos Buchwald, Daniel Kennefick, and Jurgen Renn provide further insights into the history of relativity and LIGO. The book closes with a reflection by philosopher Don Howard on the significance of Einstein's theory for the philosophy of science. Edited by Jed Buchwald, Einstein Was Right is a compelling and thought-provoking account of one of the most thrilling scientific discoveries of the modern age.

Discovering Relativity for yourself explains Einstein's Theory of Relativity to readers who are daunted by the standard mathematical approach to that profound theory. For twenty years Sam Lilley taught this subject to adults with no science background. Now he has written an explanation of the theory that demands no prior knowledge of mathematics or physics beyond an ability to do simple arithmetic. The first quarter of the book uses no more than arithmetic and a little simple geometry to introduce some of the main concepts of the theory, as well as discussing an impressive experimental test, which comes down strongly in its favour. When eventually further progress demands use of algebra and other mathematical techniques, these are carefully explained in a way that makes them accessible to absolute beginners, using many new and unorthodox methods.

This book shows how our new-found ability to observe the Earth from "the necessary distance" has wide and profound cultural and ethical implications. First of all, it is the outcome of speculations and investigations of human beings in relation to their home planet carried out over millennia. In particular, it reveals a split between the ancient idea of the Earth as nurturing mother and the more recent conception of the Earth as a neutral resource able to be infinitely exploited by humankind. The 1968 Earthrise photograph, showing the beauty and fragility of the Earth, helped spark a worldwide environmental movement; now the comprehensive coverage of global change provided by satellites has the potential to convince us beyond reasonable doubt of the huge alterations being wrought upon the Earth and its climate system as a result of human actions, and of the need to act more responsibly.

Organized by Tata Institute of Fundamental Research, Bombay

Einstein's energy-momentum relation is applicable to particles of all speeds, including the particle at rest and the massless particle moving with the speed of light. If one formula or formalism is applicable to all speeds, we say it is 'Lorentz-covariant.' As for the internal space-time symmetries, there does not appear to be a clear way to approach this problem. For a particle at rest, there are three spin degrees of freedom. For a massless particle, there are helicity and gauge degrees of freedom. The aim of this book is to present one Lorentz-covariant picture of these two different space-time symmetries. Using the same mathematical tool, it is possible to give a Lorentz-covariant picture of Gell-Mann's quark model for the proton at rest and Feynman's parton model for the fast-moving proton. The mathematical formalism for these aspects of the Lorentz covariance is based on two-by-two matrices and harmonic oscillators which serve as two basic scientific languages for many different branches of physics. It is pointed out that the formalism presented in this book is applicable to various aspects of optical sciences of current interest.

CHOICE Highly Recommended Title, August 2019 Expertly guided by renowned cosmologist Dr. David Lyth, learn about the pioneering scientists whose work provided the foundation for Einstein's formulation of his theories of relativity, and about Einstein's groundbreaking life and work as well. This highly readable and accessible panorama of the field delicately balances history and science as it takes the reader on an adventure through the centuries. Without complex mathematics or scientific formulae, this book will be of interest to all, even those without a scientific background, who are intrigued to find out more about what paved the way for one of our most famous physicists to push the boundaries of physics to new lengths. Features: Written by an internationally renowned physicist and cosmologist Describes the life and times of Einstein and his important predecessors Focuses on one of the most famous areas of science, Einstein's Relativity Theory

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Since the first French edition of the book emphasized rather the solid facts of Cosmology than the detailed discussions of controversial results, relatively few revisions were necessary for the English edition. They were made early in 1979 and affected about 5% of the text. The main revisions referred to the distance scale, the dlstribution of galaxies, the X-ray observations of clusters, the cosmic time evolution of quasars and radiogalaxies and the 3 K radiation. A new short bibliography presents the recent articles and the latest proceedings of Symposia; from these the reader can easily trace a more complete list of refer ences. I am happy to thank Professor Beiglbock for suggestions he made to improve Part lIon Spaces of Constant Curvature, and Drs. S. and J. Mitton for translating the manuscript into English. I also thank with pleasure Marie-Ange Sevin for correcting the final version. J. Heidmann March 1980, Meudon, France Preface The aim of this book is to present the fundamentals of cosmology. Its subject is the study of the universe on a grand scale: - on a grand distance scale, since from the start, we shall be escaping the con fines of our own Galaxy to explore space as far as the limits of the observable universe, some ten thousand million light years away; - and on a grand time scale, as we shall look back into the past to the very first moments of the initial expansion, about twelve thousand million years ago."

The revised and updated 2nd edition of this established textbook provides a self-contained introduction to the general theory of relativity, describing not only the physical principles and applications of the theory, but also the mathematics needed, in particular the calculus of differential forms.Updated throughout, the book contains more detailed explanations and extended discussions of several conceptual points, and strengthened mathematical deductions where required. It includes examples of work conducted in the ten years since the first edition of the book was published, for example the pedagogically helpful concept of a "river of space" and a more detailed discussion of how far the principle of relativity is contained in the general theory of relativity. Also presented is a discussion of the concept of the 'gravitational field' in Einstein's theory, and some new material concerning the 'twin paradox' in the theory of relativity. Finally, the book contains a new section about gravitational waves, exploring the dramatic progress in this field following the LIGO observations. Based on a long-established masters course, the book serves advanced undergraduate and graduate level students, and also provides a useful reference for researchers.