'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, divided in two volumes, is a rich resource for graduate students and those who wish to gain a deep knowledge of the subject without an instructor. Volume One is dedicated to the development of the theory and basic physical applications. It guides the reader from the foundation of special relativity to Einstein field equations, illustrating some basic applications in astrophysics. A detailed account of the historical and conceptual development of the theory is combined with the presentation of its mathematical foundations. Differentiable manifolds, fibre-bundles, differential forms, and the theory of connections are covered, with a sketchy introduction to homology and cohomology. (Pseudo)-Riemannian geometry is presented both in the metric and in the vielbein approach. Physical applications include the motions in a Schwarzschild field leading to the classical tests of GR (light-ray bending and periastron advance) discussion of relativistic stellar equilibrium, white dwarfs, Chandrasekhar mass limit and polytropes. An entire chapter is devoted to tests of GR and to the indirect evidence of gravitational wave emission. The formal structure of gravitational theory is at all stages compared with that of non gravitational gauge theories, as a preparation to its modern extension, namely supergravity, discussed in the second volume. 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.

This book brings together reviews from leading international authorities on the developments in the study of dark matter and dark energy, as seen from both their cosmological and particle physics side. Studying the physical and astrophysical properties of the dark components of our Universe is a crucial step towards the ultimate goal of unveiling their nature. The work developed from a doctoral school sponsored by the Italian Society of General Relativity and Gravitation. The book starts with a concise introduction to the standard cosmological model, as well as with a presentation of the theory of linear perturbations around a homogeneous and isotropic background. It covers the particle physics and cosmological aspects of dark matter and (dynamical) dark energy, including a discussion of how modified theories of gravity could provide a possible candidate for dark energy. A detailed presentation is also given of the possible ways of testing the theory in terms of cosmic microwave background, galaxy redshift surveys and weak gravitational lensing observations. Included is a chapter reviewing extensively the direct and indirect methods of detection of the hypothetical dark matter particles. Also included is a self-contained introduction to the techniques and most important results of numerical (e.g. N-body) simulations in cosmology. " This volume will be useful to researchers, PhD and graduate students in Astrophysics, Cosmology Physics and Mathematics, who are interested in cosmology, dark matter and dark energy.

The quantum and relativity theories of physics are considered to underpin all of science in an absolute sense. This monograph argues against this proposition primarily on the basis of the two theories' incompatibility and of some untenable philosophical implications of the quantum model. Elementary matter is assumed in both theories to occur as zero-dimensional point particles. In relativity theory this requires the space-like region of the underlying Minkowski space-time to be rejected as unphysical, despite its precise mathematical characterization. In quantum theory it leads to an incomprehensible interpretation of the wave nature of matter in terms of a probability function and the equally obscure concept of wave-particle duality. The most worrisome aspect about quantum mechanics as a theory of chemistry is its total inability, despite unsubstantiated claims to the contrary, to account for the fundamental concepts of electron spin, molecular structure, and the periodic table of the elements. A remedy of all these defects by reformulation of both theories as nonlinear wave models in four-dimensional space-time is described.

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.

Are we living in the "golden age" of cosmology? Are we close to understanding the nature of the unknown ingredients of the currently most accepted cosmological model and the physics of the early Universe? Or are we instead approaching a paradigm shift? What is dark matter and does it exist? How is it distributed around galaxies and clusters? Is the scientific community open to alternative ideas that may prompt a new scientific revolution - as the Copernican revolution did in Galileo's time? Do other types of supernovae exist that can be of interest for cosmology? Why have quasars never been effectively used as standard candles? Can you tell us about the scientific adventure of COBE? How does the extraction of the Cosmic Microwave Background anisotropy depend on the subtraction of the various astrophysical foregrounds? These, among many others, are the astrophysical, philosophical and sociological questions surrounding modern cosmology and the scientific community that Mauro D'Onofrio and Carlo Burigana pose to some of the most prominent cosmologists of our time. Triggered by these questions and in the spirit of Galileo's book "Dialogue Concerning the Two Chief World Systems" the roughly 40 interview partners reply in the form of essays, with a critical frankness not normally found in reviews, monographs or textbooks.

A very attractive feature of the theory of general relativity is that it is a perfectexampleofa"falsi?able"theory:notunableparameterispresentinthe theory and therefore even a single experiment incompatible with a prediction of the theory would immediately lead to its inevitable rejection, at least in the physical regime of application of the aforementioned experiment. This fact provides additional scienti?c value to one of the boldest and most fascinating achievements of the human intellect ever, and motivates a wealth of e?orts in designing and implementing tests aimed at the falsi?cation of the theory. The ?rst historical test on the theory has been the de?ection of light gr- ing the solar surface (Eddington 1919): the compatibility of the theory with this ?rst experiment together with its ability to explain the magnitude of the perihelion advance of Mercury contributed strongly to boost acceptance and worldwideknowledge.However,technologicallimitations preventedphysicists from setting up more constraining tests for several decades after the formu- tion of the theory. In fact, a relevant problem with experimental general r- ativity is that the predicted deviations from the Newtonian theory of gravity areverysmallwhentheexperimentsarecarriedoutinterrestriallaboratories.

'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.

This richly illustrated book is unique in bringing Einstein's relativity to a higher level for the non-specialist than has ever been attempted before, using nothing more than grade-school algebra. Bondi's approach with spacetime diagrams is simplified and expanded, clarifying the famous asymmetric aging-of-twins paradox. Einstein's theory of gravity, general relativity, is simplified for the reader using spacetime diagrams. The theory is applied to important topics in physics such as gravitational waves, gravitational collapse and black holes, time machines, the relationship to the quantum world, galactic motions and cosmology.

This book is a pedagogical introduction to supergravity, a gravitational field theory that includes supersymmetry (symmetry between bosons and fermions) and is a generalization of Einstein's general relativity. Supergravity provides a low-energy effective theory of superstring theory, which has attracted much attention as a candidate for the unified theory of fundamental particles, and it is a useful tool for studying non-perturbative properties of superstring theory such as D-branes and string duality. This work considers classical supergravities in four and higher spacetime dimensions with their applications to superstring theory in mind. More concretely, it discusses classical Lagrangians (or field equations) and symmetry properties of supergravities. Besides local symmetries, supergravities often have global non-compact symmetries, which play a crucial role in their applications to superstring theory. One of the main features of this book is its detailed discussion of these non-compact symmetries. The aim of the book is twofold. One is to explain the basic ideas of supergravity to those who are not familiar with it. Toward that end, the discussions are made both pedagogical and concrete by stating equations explicitly. The other is to collect relevant formulae in one place so as to be useful for applications to string theory. The subjects discussed in this book include the vielbein formulation of gravity, supergravities in four dimensions, possible types of spinors in various dimensions, superalgebras and supermultiplets, non-linear sigma models for non-compact Lie groups, electric-magnetic duality symmetries, supergravities in higher dimensions, dimensional reductions, and gauged and massive supergravities.

17 readable articles give a thorough and self-contained overview of recent developments in relativistic gravity research. The subjects covered are: gravitational lensing, the general relativistic n-body problem, observable effects in the solar system, gravitational waves and their interferometric detection, very-long-baseline interferometry, international atomic time, lunar laser- ranging measurements, measurement ofthe gravitomagnetic field of the Earth, fermion and boson stars and black holes with hair, rapidly rotating neutron stars, matter wave interferometry, and the laboratory test of Newton's law of gravity.Any scientist interested in experimentally or observatio- nally oriented relativistic gravity will read the book with profit. In addition, it is perfectly suited as a complementary text for courses on general relativity and relativistic astrophysics.

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 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 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.

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."

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.

The composition of the most remote objects brought into view by the Hubble telescope can no longer be reconciled with the nucleogenesis of standard cosmology and the alternative explanation, in terms of the -Cold-Dark-Matter model, has no recognizable chemical basis. A more rational scheme, based on the chemistry and periodicity of atomic matter, opens up an exciting new interpretation of the cosmos in terms of projective geometry and general relativity. The response of atomic structure to environmental pressure predicts non-Doppler cosmical redshifts and equilibrium nucleogenesis by -particle addition, in accord with observed periodic variation of nuclear abundance. Inferred cosmic self similarity elucidates the Bode -Titius law, general commensurability in the solar system and the occurrence of quantum phenomena on a cosmic scale. The generalized periodic function involves both matter and anti-matter in an involuted mapping to a closed projective plane. This topology ensures the same symmetrical balance in a chiral universe, wrapped around an achiral vacuum interface, without singularities. A new cosmology emerges, based on the theory of projective relativ ity, presented here as a translation of Veblen's original German text. Not only does it provide a unification of gravity, electromagnetism and quantum theory, through gauge invariance, but also supports the solution of the gravitational field equations, obtained by Goedel for a rotating universe. The appearance of an Einstein-Rosen bridge as outlet from a black hole, into conjugate anti-space, accounts for globular clusters, quasars, cosmic radiation, -ray bursters, pulsars, radio sources and other re gions of plasma activity. The effects of a multiply-connected space-time manifold on observa tions in an Euclidean tangent space are unpredictable and a complete re-assessment of the size and structure of the universe is indicated. The target readership includes scientists, as well as non-scientists - everybody with a scientific or philosophical interest in cosmology and, especially those cosmologists and mathematicians with the ability to recast the crude ideas presented here into appropriate mathematical models.

A collection of sixteen coordinated reviews on the origins of large-scale magnetic fields in the Universe, this book discusses magnetic fields in all relevant astrophysical contexts, from the interstellar medium to the scales of galaxies and clusters of galaxies. Magnetic fields are described in their very diverse environments, from stellar winds to galactic haloes and astrophysical jets; together with the roles they play in forming the structures and shaping the dynamics of these objects. Both observational evidence and its theoretical interpretations are covered up to the largest scales in the Universe. The authors are all leading scientists in their fields, making this book an authoritative, up-to-date and enduring contribution to astrophysics. This volume is aimed at graduate students and researchers in astrophysics. Previously published in Space Science Reviews journal, Vol. 166/1-4 and Vol. 169/1-4, 2012.

This book is about black holes, one of the most intriguing objects of modern theoretical physics and astrophysics. For many years, black holes have been considered as interesting solutions of the Theory of General Relativity with a number of amusing mathematical properties. Now after the discovery of astrophysical black holes, the Einstein gravity has become an important tool for their study. This self-contained textbook combines physical, mathematical, and astrophysical aspects of black hole theory. Pedagogically presented, it contains 'standard' material on black holes as well as relatively new subjects such as the role of hidden symmetries in black hole physics, and black holes in spacetimes with large extra dimensions. The book will appeal to students and young scientists interested in the theory of black holes.

THE EDITORS: DAVID L. BLOCK AND KENNETH C. FREEMAN (SOC CO-CHAIRS), IVANIO PUERARI, ROBERT GROESS AND LIZ K. BLOCK 1. Harvard College Observatory, 1958 The past century has truly brought about an explosive period of growth and discovery for the physical sciences as a whole, and for astronomy in particular. Galaxy morphology has reached a renaissance . . The year: 1958. The date: October 1. The venue: Harvard College Observatory. The lecturer: Walter Baade. With amazing foresight, Baade penned these words: "Young stars, supergiants and so on, make a terrific splash - lots of light. The total mass of these can be very small compared to the total mass of the system". Dr Layzer then asked the key question: " . . . the discussion raises the point of what this classification would look like if you were to ignore completely all the Population I, and just focus attention on the Population II . . . " We stand on the shoulders of giants. The great observer E. E. Barnard, in his pioneering efforts to photograph the Milky Way, devoted the major part of his life to identifying and numbering dusty "holes" and dust lanes in our Milky Way. No one could have dreamt that the pervasiveness of these cosmic dust masks (not only in our Galaxy but also in galaxies at high redshift) is so great, that their "penetration" is truly one of the pioneering challenges from both space-borne telescopes and from the ground.

"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.

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.

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.

This book provides a completely revised and expanded version of the previous classic edition 'General Relativity and Relativistic Astrophysics'. In Part I the foundations of general relativity are thoroughly developed, while Part II is devoted to tests of general relativity and many of its applications. Binary pulsars - our best laboratories for general relativity - are studied in considerable detail. An introduction to gravitational lensing theory is included as well, so as to make the current literature on the subject accessible to readers. Considerable attention is devoted to the study of compact objects, especially to black holes. This includes a detailed derivation of the Kerr solution, Israel's proof of his uniqueness theorem, and a derivation of the basic laws of black hole physics. Part II ends with Witten's proof of the positive energy theorem, which is presented in detail, together with the required tools on spin structures and spinor analysis. In Part III, all of the differential geometric tools required are developed in detail. A great deal of effort went into refining and improving the text for the new edition. New material has been added, including a chapter on cosmology. The book addresses undergraduate and graduate students in physics, astrophysics and mathematics. It utilizes a very well structured approach, which should help it continue to be a standard work for a modern treatment of gravitational physics. The clear presentation of differential geometry also makes it useful for work on string theory and other fields of physics, classical as well as quantum.