Unlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity.

The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semester courses in either of these subjects.

The main ideas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making "An Introduction to Riemannian Geometry" ideal for self-study.

The concept of time has fascinated humanity throughout recorded history, and it remains one of the biggest mysteries in science and philosophy. Time is clearly one of the fundamental building blocks of the universe and thus a deeper understanding of nature at a fundamental level also demands a comprehension of time. Furthermore, the origins of the universe are closely intertwined with the puzzle of time: Did time emerge at the Big Bang? Why does the arrow of time 'conspire' with the order of the initial state of the universe? This book addresses many of the most important questions about time: What is time, and is it fundamental or emergent? Why is there such an arrow of time, closely related to the initial state of the universe, and why do the cosmic, thermodynamic and other arrows agree? These issues are discussed here by leading experts, and each offers a new perspective on the debate. Their contributions delve into the most difficult research topic in physics, also describing the latest cutting edge research on the subject. The book also offers readers a comparison between the different outlooks of philosophy, physics and cosmology on the puzzle of time. This volume is intended to be useful for research purposes, but most chapters are also accessible to a more general audience of scientifically educated readers looking for deeper insights.

A major outstanding problem in physics is understanding the nature of the dark energy that is driving the accelerating expansion of the Universe. This thesis makes a significant contribution by demonstrating, for the first time, using state-of-the-art computer simulations, that the interpretation of future galaxy survey measurements is far more subtle than is widely assumed, and that a major revision to our models of these effects is urgently needed. The work contained in the thesis was used by the WiggleZ dark energy survey to measure the growth rate of cosmic structure in 2011 and had a direct impact on the design of the surveys to be conducted by the European Space Agency's Euclid mission, a 650 million euro project to measure dark energy.

The 2011 Nobel Prize in Physics was awarded for the discovery of cosmic acceleration due to dark energy, a discovery that is all the more perplexing as nobody knows what dark energy actually is. We put the modern concept of cosmological vacuum energy into historical context and show how it grew out of disparate roots in quantum mechanics (zero-point energy) and relativity theory (the cosmological constant, Einstein's "greatest blunder"). These two influences have remained strangely aloof and still co-exist in an uneasy alliance that is at the heart of the greatest crisis in theoretical physics, the cosmological-constant problem.

The search for a quantum gravity theory, a theory expected to combine the principles of general relativity and quantum theory, has led to some of the most deepest and most difficult conceptual and mathematical questions of modern physics. The present book, addressing these issues in the framework of recent versions of canonical quantization, is the first to present coherently the background for their understanding. Starting with an analysis of the structure of constrained systems and the problems of their quantization, it discusses the canonical formulation of classical relativity from different perspectives and leads to recent applications of canonical methods to create a quantum theory of gravity. The book aims to make accessible the most fundamental problems and to stimulate work in this field.

After pioneering this technology and growing the market, COMSAT fell prey to changes in government policy and to its own lack of entrepreneurial talent. The author explores the factors which contributed to this rise and fall of COMSAT.

'Gravity, a Geometrical Course' presents general relativity (GR) in a systematic and exhaustive way, covering three aspects that are homogenized into a single texture: i) the mathematical, geometrical foundations, exposed in a self consistent contemporary formalism, ii) the main physical, astrophysical and cosmological applications, updated to the issues of contemporary research and observations, with glimpses on supergravity and superstring theory, iii) the historical development of scientific ideas underlying both the birth of general relativity and its subsequent evolution. The book is divided in two volumes. Volume Two is covers black holes, cosmology and an introduction to supergravity. The aim of this volume is two-fold. It completes the presentation of GR and it introduces the reader to theory of gravitation beyond GR, which is supergravity. Starting with a short history of the black hole concept, the book covers the Kruskal extension of the Schwarzschild metric, the causal structures of Lorentzian manifolds, Penrose diagrams and a detailed analysis of the Kerr-Newman metric. An extensive historical account of the development of modern cosmology is followed by a detailed presentation of its mathematical structure, including non-isotropic cosmologies and billiards, de Sitter space and inflationary scenarios, perturbation theory and anisotropies of the Cosmic Microwave Background. The last three chapters deal with the mathematical and conceptual foundations of supergravity in the frame of free differential algebras. Branes are presented both as classical solutions of the bulk theory and as world-volume gauge theories with particular emphasis on the geometrical interpretation of kappa-supersymmetry. The rich bestiary of special geometries underlying supergravity lagrangians is presented, followed by a chapter providing glances on the equally rich collection of special solutions of supergravity. Pietro Fre is Professor of Theoretical Physics at the University of Torino, Italy and is currently serving as Scientific Counsellor of the Italian Embassy in Moscow. His scientific passion lies in supergravity and all allied topics, since the inception of the field, in 1976. He was professor at SISSA, worked in the USA and at CERN. He has taught General Relativity for 15 years. He has previously two scientific monographs, "Supergravity and Superstrings" and "The N=2 Wonderland", He is also the author of a popular science book on cosmology and two novels, in Italian.

Based on his successful work "Special Relativity and Motions Faster than Light," Moses Fayngold has written a thorough presentation of the special theory of relativity. The unique feature of the textbook is its two-leveled structure helping students to master the material more effectively: the first level presents a qualitative discussion of a problem, while the second one contains its rigorous treatment. Fayngold points out the connection between fundamental principles and known phenomena. In three new chapters on 'Relativity at Work' (Electromagnetism, Optics, Quantum Mechanics), he not only shows what relativity is, but also how it works. The scope of new material extends to include a chapter on Causality and on Applied Relativity, including astrophysical and accelerator topics. Backed throughout by numerous examples and exercises.

This book is aimed at theoretical and mathematical physicists and mathematicians interested in modern gravitational physics. I have thus tried to use language familiar to readers working on classical and quantum gravity, paying attention both to difficult calculations and to existence theorems, and discussing in detail the current literature. The first aim of the book is to describe recent work on the problem of boundary conditions in one-loop quantum cosmology. The motivation of this research was to under stand whether supersymmetric theories are one-loop finite in the presence of boundaries, with application to the boundary-value problemsoccurring in quantum cosmology. Indeed, higher-loop calculations in the absence of boundaries are already available in the litera ture, showing that supergravity is not finite. I believe, however, that one-loop calculations in the presence of boundaries are more fundamental, in that they provide a more direct check of the inconsistency of supersymmetric quantum cosmology from the perturbative point of view. It therefore appears that higher-order calculations are not strictly needed, if the one-loop test already yields negative results. Even though the question is not yet settled, this research has led to many interesting, new applications of areas of theoretical and mathematical physics such as twistor theory in flat space, self-adjointness theory, the generalized Riemann zeta-function, and the theory of boundary counterterms in super gravity. I have also compared in detail my work with results by other authors, explaining, whenever possible, the origin of different results, the limits of my work and the unsolved problems."

This book offers a presentation of the special theory of relativity that is mathematically rigorous and yet spells out in considerable detail the physical significance of the mathematics. It treats, in addition to the usual menu of topics one is accustomed to finding in introductions to special relativity, a wide variety of results of more contemporary origin. These include Zeeman s characterization of the causal automorphisms of Minkowski spacetime, the Penrose theorem on the apparent shape of a relativistically moving sphere, a detailed introduction to the theory of spinors, a Petrov-type classification of electromagnetic fields in both tensor and spinor form, a topology for Minkowski spacetime whose homeomorphism group is essentially the Lorentz group, and a careful discussion of Dirac s famous Scissors Problem and its relation to the notion of a two-valued representation of the Lorentz group. This second edition includes a new chapter on the de Sitter universe which is intended to serve two purposes. The first is to provide a gentle prologue to the steps one must take to move beyond special relativity and adapt to the presence of gravitational fields that cannot be considered negligible. The second is to understand some of the basic features of a model of the empty universe that differs markedly from Minkowski spacetime, but may be recommended by recent astronomical observations suggesting that the expansion of our own universe is accelerating rather than slowing down. The treatment presumes only a knowledge of linear algebra in the first three chapters, a bit of real analysis in the fourth and, in two appendices, some elementary point-set topology.

The first edition of the book received the 1993 CHOICE award for Outstanding Academic Title.

Reviews of first edition:

a valuable contribution to the pedagogical literature which will be enjoyed by all who delight in precise mathematics and physics. (American Mathematical Society, 1993)

Where many physics texts explain physical phenomena by means of mathematical models, here a rigorous and detailed mathematical development is accompanied by precise physical interpretations. (CHOICE, 1993)

his talent in choosing the most significant results and ordering them within the book can t be denied. The reading of the book is, really, a pleasure. (Dutch Mathematical Society, 1993)

"

The study of classical electromagnetic fields is an adventure. The theory is complete mathematically and we are able to present it as an example of classical Newtonian experimental and mathematical philosophy. There is a set of foundational experiments, on which most of the theory is constructed. And then there is the bold theoretical proposal of a field-field interaction from James Clerk Maxwell.

This textbook presents the theory of classical fields as a mathematical structure based solidly on laboratory experiments. Here the student is introduced to the beauty of classical field theory as a gem of theoretical physics. To keep the discussion fluid, the history is placed in a beginning chapter and some of the mathematical proofs in the appendices. Chapters on Green's Functions and Laplace's Equation and a discussion of Faraday's Experiment further deepen the understanding. The chapter on Einstein's relativity is an integral necessity to the text. Finally, chapters on particle motion and waves in a dispersive medium complete the picture. High quality diagrams and detailed end-of-chapter questions enhance the learning experience."

Today many scientists recognize plasma as the key element to understanding new observations in near-Earth, interplanetary, interstellar, and intergalactic space; in stars, galaxies, and clusters of galaxies, and throughout the observable universe. Physics of the Plasma Universe, 2nd Edition is an update of observations made across the entire cosmic electromagnetic spectrum over the two decades since the publication of the first edition. It addresses paradigm changing discoveries made by telescopes, planetary probes, satellites, and radio and space telescopes. The contents are the result of the author's 37 years research at Livermore and Los Alamos National Laboratories, and the U.S. Department of Energy. This book covers topics such as the large-scale structure and the filamentary universe; the formation of magnetic fields and galaxies, active galactic nuclei and quasars, the origin and abundance of light elements, star formation and the evolution of solar systems, and cosmic rays. Chapters 8 and 9 are based on the research of Professor Gerrit Verschuur, and reinvestigation of the manifestation of interstellar neutral hydrogen filaments from radio astronomical observations are given. Using data from the Green Bank 100-m telescope (GBT) of the National Radio Astronomy Observatory (NRAO), detailed information is presented for a non-cosmological origin for the cosmic microwave background quadruple moment. This volume is aimed at graduate students and researchers active in the areas of cosmic plasmas and space science. The supercomputer and experimental work was carried out within university, National laboratory, Department of Energy, and supporting NASA facilities.

"Here's a gem of a book...all peppered with delightful notes from science fiction films, novels, and comics. I can't turn a page without finding a jewel." Clifford Stoll, University of California, Berkeley, author of The Cuckoo's Egg "The research that has gone into this book is impressive." Nature "For professional physicists much of the value lies in the extensive technical appendices and footnotes, and the exhaustive list of references. But if, like me, you are a child at heart, the real fun lies in the zany stories and wild speculations." Physics World Time Machines explores the idea of time travel from the first account in English literature to the latest theories of physicists such as Kip Thorne and Igor Novikov. This very readable work covers a variety of topics including the history of time travel in fiction; the fundamental scientific concepts of time, spacetime, and the fourth dimension; the speculations of Einstein, Richard Feynman, Kurt Goedel, and others; time travel paradoxes, and much more.

In this book, the author leads the reader, step by step and without any advanced mathematics, to a clear understanding of the foundations of modern elementary particle physics and cosmology. He also addresses current and controversial questions on topics such as string theory. The book contains gentle introductions to the theories of special and general relativity, and also classical and quantum field theory. The essential aspects of these concepts are understood with the help of simple calculations; for example, the force of gravity as a consequence of the curvature of the space-time. Also treated are the Big Bang, dark matter and dark energy, as well as the presently known interactions of elementary particles: electrodynamics, the strong and the weak interactions including the Higgs boson. Finally, the book sketches as yet speculative theories: Grand Unification theories, supersymmetry, string theory and the idea of additional dimensions of space-time. Since no higher mathematical or physics expertise is required, the book is also suitable for college and university students at the beginning of their studies. Hobby astronomers and other science enthusiasts seeking a deeper insight than can be found in popular treatments will also appreciate this unique book.

Through examining the work of W. B. Yeats, James Joyce, and Samuel Beckett, Katherine Ebury shows cosmology had a considerable impact on modernist creative strategies, developing alternative reading models of difficult texts such as Finnegans Wake and 'The Trilogy'.

The 1994 Cargese Summer Institute on Frontiers in Partide Physics was organized by the Universite Pierre et Marie Curie, Paris (M. Levy), the Ecole Normale Superieure, Paris (J. Iliopoulos), the Katholieke Universiteit Leuven (R. Gastmans), and the Uni- versite Catholique de Louvain (J. -M. Gerard), which, since 1975, have joined their efforts and worked in common. It was the eleventh Summer Institute on High Energy Physics organized jointly at Cargese by three of these universities. Severa! new frontiers in partide physics were thoroughly discussed at this school. the new euergy range in deep-iuelastic electron-proton scattering is beiug In particular, explored by HERA (DESY, Hamburg), and Professor A. De Roeck described the first results from the H1 and Zeus experiments, while Professors A. H. Mueller aud Z. Kuuszt discussed their relevance from the theoretical point of view. Also, the satellite exper- iments offer new possibilities for exploring the links between astrophysics, cosmology, and partide physics. A critica] a. nalysis of these experiments was performed by Pro- fessor B. Sadoulet, and Professor M. Spiro made the connection with the results from earth-based neutrino experiments. Finally, much attentiou was giveu to the latest re- sults from the TEVATRON (Fermilab, USA), showing further evidence for the loug awaited top quark. Professor A. Tollestrup gave a detailed presentation of these results aud discussed their importance for the Standard Model.

This thesis is based on the first data from the Large Hadron Collider (LHC) at CERN. Its theme can be described as the classical Rutherford scattering experiment adapted to the LHC: measurement of scattering angles to search for new physics and substructure. At the LHC, colliding quarks and gluons exit the proton collisions as collimated particle showers, or jets. The thesis presents studies of the scattering angles of these jets. It includes a phenomenological study at the LHC design energy of 14 TeV, where a model of so-called large extra dimensions is used as a benchmark process for the sensitivity to new physics. The experimental result is the first measurement, made in 2010, by ATLAS, operating at the LHC start-up energy of 7 TeV. The result is compatible with the Standard Model and demonstrates how well the physics and the apparatus are understood. The first data is a tiny fraction of what will be accumulated in the coming years, and this study has set the stage for performing these measurements with confidence as the LHC accumulates luminosity and increases its energy, thereby probing smaller length scales.

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 . . *. . . *. . . **. . . ****. . . *****. . . *. *. *. . *. . . . *. . *. *. . . **. ***.

This collection of articles gives a nice overview of the fast growing field of diffusion and transport. The area of non-Browman statistical mechanics has many extensions into other fields like biology, ecology, geophysics etc. These tutorial lectures address e.g. Levy flights and walks, diffusion on metal surfaces or in superconductors, classical diffusion, biased and anomalous diffusion, chemical reaction diffusion, aging in glassy systems, diffusion in soft matter and in nonsymmetric potentials, and also new problems like diffusive processes in econophysics and in biology."

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.

"General Relativity Without Calculus" offers a compact but mathematically correct introduction to the general theory of relativity, assuming only a basic knowledge of high school mathematics and physics. Targeted at first year undergraduates (and advanced high school students) who wish to learn Einstein's theory beyond popular science accounts, it covers the basics of special relativity, Minkowski space-time, non-Euclidean geometry, Newtonian gravity, the Schwarzschild solution, black holes and cosmology. The quick-paced style is balanced by over 75 exercises (including full solutions), allowing readers to test and consolidate their understanding.

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 Hidden Hypotheses Behind the Big Bang It is quite unavoidable that many philosophical a priori assumptions lurk behind the debate between supporters of the Big Bang and the anti-BB camp. The same battle has been waged in physics between the determinists and the opposing viewpoint. Therefore, by way of introduction to this symposium, I would like to discuss, albeit briefly, the many "hypotheses", essentially of a metaphysical nature, which are often used without being clearly stated. The first hypothesis is the idea that the Universe has some origin, or origins. Opposing this is the idea that the Universe is eternal, essentially without beginning, no matter how it might change-the old Platonic system, opposed by an Aristote lian view! Or Pope Pius XII or Abbe Lemaitre or Friedmann versus Einstein or Hoyle or Segal, etc. The second hypothesis is the need for a "minimum of hypotheses" -the sim plicity argument. One is expected to account for all the observations with a mini mum number of hypotheses or assumptions. In other words, the idea is to "save the phenomena", and this has been an imperative since the time of Plato and Aristotle. But numerous contradictions have arisen between the hypotheses and the facts. This has led some scientists to introduce additional entities, such as the cosmologi cal constant, dark matter, galaxy mergers, complicated geometries, and even a rest mass for the photon. Some of the proponents of the latter idea were Einstein, de Broglie, Findlay-Freundlich, and later Vigier and myself.