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.

This book is an elaboration of lecture notes for the graduate course on General Rela tivity given by the author at Boston University in the spring semester of 1972. It is an introduction to the subject only, as the time available for the course was limited. The author of an introduction to General Relativity is faced from the beginning with the difficult task of choosing which material to include. A general criterion as sisting in this choice is provided by the didactic character of the book: Those chapters have to be included in priority, which will be most useful to the reader in enabling him to understand the methods used in General Relativity, the results obtained so far and possibly the problems still to be solved. This criterion is not sufficient to ensure a unique choice. General Relativity has developed to such a degree, that it is impossible to include in an introductory textbook of a reasonable length even a very condensed treatment of all important problems which have been discussed until now and the author is obliged to decide, in a more or less subjective manner, which of the more recent developments to omit. The following lines indicate by means of some examples the kind of choice made in this book."

This modern introduction to particle physics equips students with the skills needed to develop a deep and intuitive understanding of the physical theory underpinning contemporary experimental results. The fundamental tools of particle physics are introduced and accompanied by historical profiles charting the development of the field. Theory and experiment are closely linked, with descriptions of experimental techniques used at CERN accompanied by detail on the physics of the Large Hadron Collider and the strong and weak forces that dominate proton collisions. Recent experimental results are featured, including the discovery of the Higgs boson. Equations are supported by physical interpretations, and end-of-chapter problems are based on datasets from a range of particle physics experiments including dark matter, neutrino, and collider experiments. A solutions manual for instructors is available online. Additional features include worked examples throughout, a detailed glossary of key terms, appendices covering essential background material, and extensive references and further reading to aid self-study, making this an invaluable resource for advanced undergraduates in physics.

This compact guide presents the key features of general relativity, to support and supplement the presentation in mainstream, more comprehensive undergraduate textbooks, or as a re-cap of essentials for graduate students pursuing more advanced studies. It helps students plot a careful path to understanding the core ideas and basics of differential geometry, as applied to general relativity, without overwhelming them. While the guide doesn't shy away from necessary technicalities, it emphasises the essential simplicity of the main physical arguments. Presuming a familiarity with special relativity (with a brief account in an appendix), it describes how general covariance and the equivalence principle motivate Einstein's theory of gravitation. It then introduces differential geometry and the covariant derivative as the mathematical technology which allows us to understand Einstein's equations of general relativity. The book is supported by numerous worked exampled and problems, and important applications of general relativity are described in an appendix.

BY W. H. MCCREA, F. R. S. 'THE only justification for our concepts and system of concepts is that they serve to represent the complex of our experiences; beyond this they have no legitimacy. ' So Einstein writes on page 2 of this book. Most present-day physicists would agree, and many before Einstein must have held the same opinion. Einstein, however, put the opinion into practice to better purpose than any physicist before him. And for Einstein it evidently meant what it means for most of us today: a theory is the construction of a theoretical model of the world of physics; all the mathematical discussion applies to the model; the model embodies the 'system of concepts', and it serves 'to represent the complex of our experiences' if the experience of the theoretical observer in the theoretical model can be put into satisfactory correspondence with the experi- ence of the actual observer in the actual physical world. Classical mechanics and classical electromagnetism pro- vide models that are good representations of two sets of actual experiences. As Einstein was the first fully to appreciate, however, it is not possible to combine these into a single self-consistent model. The construction of the simplest possible self-consistent model is the achieve- ment of Einstein's theory of special relativity. The theory is found, in particular, to give a satisfactory representation of the electromagnetic interaction between charged particles through its use of the concept of the electromagnetic field.

The education Research Center at the Massachusetts Institute of Technology (formerly the Science Teaching Center) was established to study the process of instruction, aids thereto, and the learning process itself, with special reference to science teaching at the university level. Generous support from the National Science Foundation and from the Kettering, Shell, Victoria, W. T. Grant, and Bing Foundations provided the means for assembling and maintaining an experienced staff to cooperate with members of the Institute's Physics Department in the examination, improvement, and development of physics curriculum materials for students planning a career in the sciences.

After careful analysis of objectives and the problems involved, preliminary versions of textbooks were prepared, tested through classroom use at M.I.T. and other institutions, re-evaluated, rewritten, and tried again. Only then were the final manuscripts undertaken.

In general the books in the series will be brief. Most may be covered in a single term or less. Each will be available in either cloth or paper binding. Their brevity and structure (as well as their reasonable price) will make it possible for teachers to select topics and organize courses according to individual needs and preferences.

As we navigate through life we instinctively model time as having a flowing present that divides a fixed past from open future. This model develops in childhood and is deeply saturated within our language, thought and behavior, affecting our conceptions of the universe, freedom and the self. Yet as central as it is to our lives, physics seems to have no room for this flowing present. What Makes Time Special? demonstrates this claim in detail and then turns to two novel positive tasks. First, by looking at the world "sideways" - in the spatial directions - it shows that physics is not "spatializing time" as is commonly alleged. Even relativity theory makes significant distinctions between the spacelike and timelike directions, often with surprising consequences. Second, if the flowing present is an illusion, it is a deep one worthy of explanation. The author develops a picture whereby the temporal flow arises as an interaction effect between an observer and the physics of the world. Using insights from philosophy, cognitive science, biology, psychology and physics, the theory claims that the flowing present model of time is the natural reaction to the perceptual and evolutionary challenges thrown at us. Modeling time as flowing makes sense even if it misrepresents it.

"Flatland" is a unique, delightful satire that has charmed readers for over a century. Published in 1884 by the English clergyman and headmaster Edwin A. Abbott, it is the fanciful tale of A. Square, a two-dimensional being who is whisked away by a mysterious visitor to The Land of Three Dimensions, an experience that forever alters his worldview.

Like the original, Ian Stewart's commentary takes readers on a strange and wonderful journey. With clarity and wit, Stewart illuminates Abbott's numerous Victorian references and touches on such diverse topics as ancient Babylon, Karl Marx, Mary Shelley's "Frankenstein," Mt. Everest, H.G. Wells, and phrenology. "The Annotated Flatland" makes fascinating connections between "Flatland" and Abbott's era, resulting in a classic to rival Abbott's own, and a book that will inspire and delight curious readers for generations to come.

The problem of quantum gravity is often viewed as the most pressing unresolved problem of modern physics: our theories of spacetime and matter, described respectively by general relativity (Einstein's theory of gravitation and spacetime) and quantum mechanics (our best theory of matter and the other forces of nature) resist unification. Covered with Deep Mist provides the first book-length treatment of the history of quantum gravity, focusing on its origins and earliest stages of development until the mid-1950s. Readers will be guided through the impacts on the problem of quantum gravity resulting from changes in the two ingredient theories, quantum theory and general relativity, which were themselves still under construction in the years studied. We examine how several of the core approaches of today were formed in an era when the field was highly unfashionable. The book aims to be accessible to a broad range of readers and goes beyond a merely technical examination to include social and cultural factors involved in the changing fortunes of the field. Suitable for both newcomers and seasoned quantum gravity professionals, the book will shine new light on this century-old, unresolved problem.

There is little doubt that Einstein's theory of relativity captures the imagination. Not only has it radically altered the way we view the universe, but the theory also has a considerable number of surprises in store. This is especially so in the three main topics of current interest that this book reaches, namely: black holes, gravitational waves, and cosmology. The main aim of this textbook is to provide students with a sound mathematical introduction coupled to an understanding of the physical insights needed to explore the subject. Indeed, the book follows Einstein in that it introduces the theory very much from a physical point of view. After introducing the special theory of relativity, the basic field equations of gravitation are derived and discussed carefully as a prelude to first solving them in simple cases and then exploring the three main areas of application. This new edition contains a substantial extension content that considers new and updated developments in the field. Topics include coverage of the advancement of observational cosmology, the detection of gravitational waves from colliding black holes and neutron stars, and advancements in modern cosmology. Einstein's theory of relativity is undoubtedly one of the greatest achievements of the human mind. Yet, in this book, the author makes it possible for students with a wide range of abilities to deal confidently with the subject. Based on both authors' experience teaching the subject this is achieved by breaking down the main arguments into a series of simple logical steps. Full details are provided in the text and the numerous exercises while additional insight is provided through the numerous diagrams. As a result this book makes an excellent course for any reader coming to the subject for the first time while providing a thorough understanding for any student wanting to go on to study the subject in depth

This is the first comprehensive treatment of active galactic nuclei--the cosmic powerhouses at the core of many distant galaxies. The term "active galactic nuclei" refers to quasars, radio galaxies, Seyfert galaxies, blazars, and related objects, all of which are believed to share a similar central engine--a supermassive black hole many times the mass of the Sun. Astrophysicists have studied these phenomena for the past several decades and have begun to develop a consensus about many of their properties and internal mechanisms. Julian Krolik, one of the world's leading authorities on the subject, sums up leading ideas from across the entire range of research, making this book an invaluable resource for astronomers, physicists interested in applications of the theory of gravitation, and graduate students.

Krolik begins by addressing basic questions about active galactic nuclei: What are they? How can they be found? How do they evolve? He assesses the evidence for massive black holes and considers how they generate power by accretion. He discusses X-ray and g-ray emission, radio emission and jets, emission and absorption lines, anisotropic appearance, and the relationship between an active nucleus and its host galaxy. He explores the mysteries of what ignites, fuels, and extinguishes active galactic nuclei, and concludes with a general review of where the field now stands. The book is unique in paying careful attention to relevant physics as well as astronomy, reflecting in part the importance of general relativity to understanding active galactic nuclei. Clear, authoritative, and detailed, this is crucial reading for anyone interested in one of the most dynamic areas of astrophysics today.

This comprehensive student manual has been designed to accompany the leading textbook by Bernard Schutz, A First Course in General Relativity, and uses detailed solutions, cross-referenced to several introductory and more advanced textbooks, to enable self-learners, undergraduates and postgraduates to master general relativity through problem solving. The perfect accompaniment to Schutz's textbook, this manual guides the reader step-by-step through over 200 exercises, with clear easy-to-follow derivations. It provides detailed solutions to almost half of Schutz's exercises, and includes 125 brand new supplementary problems that address the subtle points of each chapter. It includes a comprehensive index and collects useful mathematical results, such as transformation matrices and Christoffel symbols for commonly studied spacetimes, in an appendix. Supported by an online table categorising exercises, a Maple worksheet and an instructors' manual, this text provides an invaluable resource for all students and instructors using Schutz's textbook.

Do something amazing and learn a new skill thanks to the Little Ways to Live a Big Life books! The beginning of the 20th century heralded a scientific revolution: what a few brilliant minds uncovered about our reality in the first twenty years has shaped the history of our species. And one of them in particular stands out: Einstein, with his celebrated E=mc2. In this remarkable and insightful book, Christophe Galfard describes how E=mc2 is a direct consequence of the Theory of Special Relativity, the theory of how objects move and behave, at speeds close to the speed of light. He considers Einstein's legacy in the light of the 21st century, with fresh hindsight, and considers its impact on our vision of reality. The reader will discover that far from being just a formula, it is a brand new understanding of the nature of space and time. Some of the greatest scientific breakthroughs in the history of science have been made by geniuses who managed to merge and unite hitherto separated domains of knowledge. Galfard explores two unifications with Einstein's theories, and looks at the even bigger picture of how E=mc2 has changed our world, and what it entails for the future. Throughout, Galfard takes the reader on an extremely entertaining journey, using simple, jargon-free language to help the reader gain a deeper understanding of science. With humour and patience, he guides us through the world of particles, anti-matter and much more to bring us closer to an ultimate understanding of reality as we understand it today.

Following on from a previous volume on Special Relativity, Andrew Steane's second volume on General Relativity and Cosmology is aimed at advanced undergraduate or graduate students undertaking a physics course, and encourages them to expand their knowledge of Special Relativity. Beginning with a survey of the main ideas, the textbook goes on to give the methodological foundations to enable a working understanding of astronomy and gravitational waves (linearized approximation, differential geometry, covariant differentiation, physics in curved spacetime). It covers the generic properties of horizons and black holes, including Hawking radiation, introduces the key concepts in cosmology and gives a grounding in classical field theory, including spinors and the Dirac equation, and a Lagrangian approach to General Relativity. The textbook is designed for self-study and is aimed throughout at clarity, physical insight, and simplicity, presenting explanations and derivations in full, and providing many explicit examples.

Applications of quantum field theoretical methods to gravitational physics, both in the semiclassical and the full quantum frameworks, require a careful formulation of the fundamental basis of quantum theory, with special attention to such important issues as renormalization, quantum theory of gauge theories, and especially effective action formalism. The first part of this graduate textbook provides both a conceptual and technical introduction to the theory of quantum fields. The presentation is consistent, starting from elements of group theory, classical fields, and moving on to the effective action formalism in general gauge theories. Compared to other existing books, the general formalism of renormalization in described in more detail, and special attention paid to gauge theories. This part can serve as a textbook for a one-semester introductory course in quantum field theory. In the second part, we discuss basic aspects of quantum field theory in curved space, and perturbative quantum gravity. More than half of Part II is written with a full exposition of details, and includes elaborated examples of simplest calculations. All chapters include exercises ranging from very simple ones to those requiring small original investigations. The selection of material of the second part is done using the "must-know" principle. This means we included detailed expositions of relatively simple techniques and calculations, expecting that the interested reader will be able to learn more advanced issues independently after working through the basic material, and completing the exercises.

As we navigate through life we instinctively model time as having a flowing present that divides a fixed past from open future. This model develops in childhood and is deeply saturated within our language, thought and behavior, affecting our conceptions of the universe, freedom and the self. Yet as central as it is to our lives, physics seems to have no room for this flowing present. What Makes Time Special? demonstrates this claim in detail and then turns to two novel positive tasks. First, by looking at the world "sideways" - in the spatial directions - it shows that physics is not "spatializing time" as is commonly alleged. Even relativity theory makes significant distinctions between the spacelike and timelike directions, often with surprising consequences. Second, if the flowing present is an illusion, it is a deep one worthy of explanation. The author develops a picture whereby the temporal flow arises as an interaction effect between an observer and the physics of the world. Using insights from philosophy, cognitive science, biology, psychology and physics, the theory claims that the flowing present model of time is the natural reaction to the perceptual and evolutionary challenges thrown at us. Modeling time as flowing makes sense even if it misrepresents it.

Einstein's general theory of relativity is introduced in this advanced undergraduate and beginning graduate level textbook. Topics include special relativity, in the formalism of Minkowski's four-dimensional space-time, the principle of equivalence, Riemannian geometry and tensor analysis, Einstein field equation, as well as many modern cosmological subjects, from primordial inflation and cosmic microwave anisotropy to the dark energy that propels an accelerating universe.
The author presents the subject with an emphasis on physical examples and simple applications without the full tensor apparatus. The reader first learns how to describe curved spacetime. At this mathematically more accessible level, the reader can already study the many interesting phenomena such as gravitational lensing, precession of Mercury's perihelion, black holes, and cosmology. The full tensor formulation is presented later, when the Einstein equation is solved for a few symmetric cases. Many modern topics in cosmology are discussed in this book: from inflation, cosmic microwave anisotropy to the "dark energy" that propels an accelerating universe.
Mathematical accessibility, together with the various pedagogical devices (e.g., worked-out solutions of chapter-end problems), make it practical for interested readers to use the book to study general relativity and cosmology on their own.

General relativity is now an essential part of undergraduate and graduate courses in physics, astrophysics and applied mathematics. This simple, user-friendly introduction to relativity is ideal for a first course in the subject. Beginning with a comprehensive but simple review of special relativity, the book creates a framework from which to launch the ideas of general relativity. After describing the basic theory, it moves on to describe important applications to astrophysics, black hole physics, and cosmology. Several worked examples, and numerous figures and images, help students appreciate the underlying concepts. There are also 180 exercises which test and develop students' understanding of the subject. The textbook presents all the necessary information and discussion for an elementary approach to relativity. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521735612.

During the last years of his life Einstein tried unsuccessfully to unify electromagnetic force with gravitational force geometrically. The nearest he got was through the ideas of Kaluza and Klein who appended a tiny fifth commuting coordinate to spacetime. Researchers have followed in those footsteps by adding at least six more such minuscule coordinates so as to incorporate the other forces of nature, culminating in string theory - which has unfortunately not met with experimental support. Other proposals have likewise failed or are still waiting to be confirmed experimentally.The author shows that one can successfully unify gravity with electromagnetism geometrically by adding a single complex anticommuting coordinate to spacetime, which can be associated with the property of 'electricity'. By adding extra four anticommuting properties ('chromicity' and 'neutrinicity'), associated with strong and weak interactions, one can get a unified picture of all the natural forces and particles including the 'standard model': The whole construct relies upon the full specification of events and automatically allows for replication of particle families. The monograph traces the history of attempts of unification before explaining the author's 'where-when-what' scheme.

A new title in the Manchester Physics Series, this introductory text emphasises physical principles behind classical mechanics and relativity. It assumes little in the way of prior knowledge, introducing relevant mathematics and carefully developing it within a physics context. Designed to provide a logical development of the subject, the book is divided into four sections, introductory material on dynamics, and special relativity, which is then followed by more advanced coverage of dynamics and special relativity. Each chapter includes problems ranging in difficulty from simple to challenging with solutions for solving problems. Includes solutions for solving problems Numerous worked examples included throughout the book Mathematics is carefully explained and developed within a physics environment Sensitive to topics that can appear daunting or confusing