Essential mathematical insights into one of the most important and challenging open problems in general relativity—the stability of black holes One of the major outstanding questions about black holes is whether they remain stable when subject to small perturbations. An affirmative answer to this question would provide strong theoretical support for the physical reality of black holes. In this book, Sergiu Klainerman and Jérémie Szeftel take a first important step toward solving the fundamental black hole stability problem in general relativity by establishing the stability of nonrotating black holes—or Schwarzschild spacetimes—under so-called polarized perturbations. This restriction ensures that the final state of evolution is itself a Schwarzschild space. Building on the remarkable advances made in the past fifteen years in establishing quantitative linear stability, Klainerman and Szeftel introduce a series of new ideas to deal with the strongly nonlinear, covariant features of the Einstein equations. Most preeminent among them is the general covariant modulation (GCM) procedure that allows them to determine the center of mass frame and the mass of the final black hole state. Essential reading for mathematicians and physicists alike, this book introduces a rich theoretical framework relevant to situations such as the full setting of the Kerr stability conjecture.

Essential mathematical insights into one of the most important and challenging open problems in general relativity-the stability of black holes One of the major outstanding questions about black holes is whether they remain stable when subject to small perturbations. An affirmative answer to this question would provide strong theoretical support for the physical reality of black holes. In this book, Sergiu Klainerman and Jeremie Szeftel take a first important step toward solving the fundamental black hole stability problem in general relativity by establishing the stability of nonrotating black holes-or Schwarzschild spacetimes-under so-called polarized perturbations. This restriction ensures that the final state of evolution is itself a Schwarzschild space. Building on the remarkable advances made in the past fifteen years in establishing quantitative linear stability, Klainerman and Szeftel introduce a series of new ideas to deal with the strongly nonlinear, covariant features of the Einstein equations. Most preeminent among them is the general covariant modulation (GCM) procedure that allows them to determine the center of mass frame and the mass of the final black hole state. Essential reading for mathematicians and physicists alike, this book introduces a rich theoretical framework relevant to situations such as the full setting of the Kerr stability conjecture.

DROPOUT. PACIFIST. PHYSICIST. CASANOVA. REFUGEE. REBEL. GENIUS. THINK YOU KNOW EINSTEIN? THINK AGAIN His face is instantly recognisable. His name is shorthand for genius. Today, he's a figurehead as much as a man, symbolic of things larger than himself: of scientific progress, of the human mind, even of the age. But who was Einstein really? The Nobel Prize-winning physicist who discovered relativity, black holes and E = mc2, dined with Charlie Chaplin in Hollywood and was the inspiration for (highly radioactive) element 99, Albert Einstein was also a high school dropout with an FBI file 1,400 pages long. In this book, Samuel Graydon brings history's most famous scientist back to life. From his lost daughter to escaping the Nazis, from his love letters to unlikely inventions, from telling jokes to cheer up his sad parrot Bibo to refusing the Presidency of Israel, through the discoveries and thought experiments that changed science, Einstein in Time and Space tells 99 unforgettable stories of the man who redefined how we view our universe and our place within it.

The standard starting point in cosmology is the cosmological principle; the assumption that the universe is spatially homogeneous and isotropic. After imposing this assumption, the only freedom left, as far as the geometry is concerned, is the choice of one out of three permissible spatial geometries, and one scalar function of time. Combining the cosmological principle with an appropriate description of the matter leads to the standard models. It is worth noting that these models yield quite a successful description of our universe. However, even though the universe may, or may not, be almost spatially homogeneous and isotropic, it is clear that the cosmological principle is not exactly satisfied. This leads to several questions. The most natural one concerns stability: given initial data corresponding to an expanding model of the standard type, do small perturbations give rise to solutions that are similar to the future? Another question concerns the shape of the universe: what are the restrictions if we only assume the universe to appear almost spatially homogeneous and isotropic to every observer? The main purpose of the book is to address these questions. However, to begin with, it is necessary to develop the general theory of the Cauchy problem for the Einstein-Vlasov equations. In order to to make the results accessible to researchers who are not mathematicians, but who are familiar with general relativity, the book contains an extensive prologue putting the results into a more general context.

This book describes the basic concepts of supersymmetric theories. It is aimed at theorists, experimentalists and cosmologists interested in supersymmetry, and its content is correspondingly divided into three distinct tracks of study. The topics covered include a discussion of the motivation for supersymmetry in fundamental physics, a description of the minimal supersymmetric model as well as models of grand unification and string models, a presentation of the main scenarios for supersymmetry breaking, including the concepts and results of dynamical breaking. On the astrophysics/cosmology side, the book includes discussions of supersymmetric dark matter candidates, inflation, dark energy, and the cosmological constant problem. Some very basic knowledge of quantum field theory is needed and extensive appendices (in particular an introduction to the Standard Model of fundamental interactions) allow the reader to refresh and complete their notions.

This is the single most complete guide to Albert Einstein's life and work for students, researchers, and browsers alike. Written by three leading Einstein scholars who draw on their combined wealth of expertise gained during their work on the Collected Papers of Albert Einstein, this authoritative and accessible reference features more than one hundred entries and is divided into three parts covering the personal, scientific, and public spheres of Einstein's life. An Einstein Encyclopedia contains entries on Einstein's birth and death, family and romantic relationships, honors and awards, educational institutions where he studied and worked, citizenships and immigration to America, hobbies and travels, plus the people he befriended and the history of his archives and the Einstein Papers Project. Entries on Einstein's scientific theories provide useful background and context, along with details about his assistants, collaborators, and rivals, as well as physics concepts related to his work. Coverage of Einstein's role in public life includes entries on his Jewish identity, humanitarian and civil rights involvements, political and educational philosophies, religion, and more. Commemorating the hundredth anniversary of the theory of general relativity, An Einstein Encyclopedia also includes a chronology of Einstein's life and appendixes that provide information for further reading and research, including an annotated list of a selection of Einstein's publications and a review of selected books about Einstein. * More than 100 entries cover the rich details of Einstein's personal, professional, and public life* Authoritative entries explain Einstein's family relationships, scientific achievements, political activities, religious views, and more* More than 40 illustrations include photos of Einstein and his circle plus archival materials* A chronology of Einstein's life, appendixes, and suggestions for further reading provide essential details for further research

This book provides an accessible introduction to loop quantum gravity and some of its applications, at a level suitable for undergraduate students and others with only a minimal knowledge of college level physics. In particular it is not assumed that the reader is familiar with general relativity and only minimally familiar with quantum mechanics and Hamiltonian mechanics. Most chapters end with problems that elaborate on the text, and aid learning. Applications such as loop quantum cosmology, black hole entropy and spin foams are briefly covered. The text is ideally suited for an undergraduate course in the senior year of a physics major. It can also be used to introduce undergraduates to general relativity and quantum field theory as part of a 'special topics' type of course.
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Special relativity provides the foundations of our knowledge of space and time. Without it, our understanding of the world, and its place in the universe, would be unthinkable. This book gives a concise, elementary, yet exceptionally modern, introduction to special relativity. It is a gentle yet serious 'first encounter', in that it conveys a true understanding rather than purely reports the basic facts. Only very elementary mathematical knowledge is needed to master it (basic high-school maths), yet it will leave the reader with a sound understanding of the subject. Special Relativity: A First Encounter starts with a broad historical introduction and motivation of the basic notions. The central chapters are dedicated to special relativity, mainly following Einstein's historical route. Later chapters turn to various applications in all parts of physics and everyday life. Unlike other books on the subject, the current status of the experimental foundations of special relativity is accurately reported and the experiments explained. This book will appeal to anyone wanting a introduction to the subject, as well as being background reading for students beginning a course in physics.

A concise introduction to the greatest questions of modern cosmology. What came before the big bang? How will the universe evolve into the future? Will there be a big crunch? Questions like these have no definitive answers, but there are many contending theories. In A Little Book about the Big Bang, physicist and writer Tony Rothman guides expert and uninitiated readers alike through the most compelling mysteries surrounding the nature and origin of the universe. Cosmologists are busy these days, actively researching dark energy, dark matter, and quantum gravity, all at the foundation of our understanding of space, time, and the laws governing the universe. Enlisting thoughtful analogies and a step-by-step approach, Rothman breaks down what is known and what isn't and details the pioneering experimental techniques scientists are bringing to bear on riddles of nature at once utterly basic and stunningly complex. In Rothman's telling, modern cosmology proves to be an intricate web of theoretical predictions confirmed by exquisitely precise observations, all of which make the theory of the big bang one of the most solid edifices ever constructed in the history of science. At the same time, Rothman is careful to distinguish established physics from speculation, and in doing so highlights current controversies and avenues of future exploration. The idea of the big bang is now almost a century old, yet with each new year comes a fresh enigma. That is scientific progress in a nutshell: every groundbreaking discovery, every creative explanation, provokes new and more fundamental questions. Rothman takes stock of what we have learned and encourages readers to ponder the mysteries to come.

Professor Sir Roger Penrose's work, spanning fifty years of science, with over five thousand pages and more than three hundred papers, has been collected together for the first time and arranged chronologically over six volumes, each with an introduction from the author. Where relevant, individual papers also come with specific introductions or notes. Among the new developments that occurred during this period was the introduction of a particular notion of 'quasi-local mass-momentum and angular momentum', the topic of Penrose's Royal Society paper. Many encouraging results were initially obtained but, later, difficulties began to emerge and remain today. Also, an extensive paper (with Eastwood and Wells) gives a thorough account of the relation between twistor cohomology and massless fields. This volume witnesses Penrose's increasing conviction that the puzzling issue of quantum measurement could only be resolved by the appropriate unification of quantum mechanics with general relativity, where that union must involve an actual change in the rules of quantum mechanics as well as in space-time structure. Penrose's first incursions into a possible relation between consciousness and quantum state reduction are also covered here.

Professor Sir Roger Penrose's work, spanning fifty years of science, with over five thousand pages and more than three hundred papers, has been collected together for the first time and arranged chronologically over six volumes, each with an introduction from the author. Where relevant, individual papers also come with specific introductions or notes. This sixth volume describes an actual experiment to measure the length of time that a quantum superposition might last (developing the Diosi-Penrose proposal). It also discusses the significant progress made in relation to incorporating the 'googly' information for a gravitational field into the structure of a curved twistor space. Penrose also covers such things as the geometry of light rays in relation to twistor-space structures, the utility of complex numbers in drawing three-dimensional shapes, and the geometrical representation of different types of musical scales. The turn of the millennium was also an opportunity to reflect on progress in many areas up until that point.

Based on the author's own work and results obtained by renowned cosmologists, this short book provides a concise introduction to the relatively new research field of cosmological thermodynamics. Starting with a brief overview of basic cosmology and thermodynamics, the text gives an interesting account of the application of horizon thermodynamics to the homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) model, the inhomogeneous (Lemaitre-Tolman-Bondi) LTB model, and the gravitationally induced adiabatic particle creation scenario which is considered to be a viable alternative to the concordance Lambda-CDM model of the Universe. Both seasoned and new researchers in this field will appreciate the lucid presentation and the rich bibliography.

Relativity has much to offer for a well-rounded education. Yet books on relativity either assume a strong background in physics and math, aimed at advanced physics students, or, alternatively, offer a broad description with little intellectual challenge. This book bridges the gap. It aims at readers with essentially no physics or math background, who still find it rewarding to think rigorously. The book takes a "thinking tools" approach, by first making readers comfortable with a new thinking tool and then applying it to learn more about how nature works. By the end of the book, readers will have collected a versatile toolbox and will be comfortable using the tools to think about and really understand the intriguing phenomena they may have only heard about, including the twin paradox, black holes, and time travel. End-of-chapter exercises span a range of difficulty, allowing adventurous readers to stretch their understanding further as desired. Students who have studied, or are studying, relativity at a more mathematical level will also find the book useful for a more conceptual understanding.

To those of us who are not mathematicians or physicists, Einstein's theory of relativity often seems incomprehensible, exotic, and of little real-world use. None of this is true. Daniel F. Styer's introduction to the topic not only shows us why these beliefs are mistaken but also shines a bright light on the subject so that any curious-minded person with an understanding of algebra and geometry can both grasp and apply the theory.

Styer starts off slowly and proceeds carefully, explaining the concepts undergirding relativity in language comprehensible to nonscientists yet precise and accurate enough to satisfy the most demanding professional. He demonstrates how the theory applies to various real-life situations with easy equations and simple, clear diagrams. Styer's classroom-tested method of conveying the core ideas of relativity--the relationship among and between time, space, and motion and the behavior of light--encourages questions and shows the way to finding the answers. Each of the book's four parts builds on the sections that come before, leading the reader by turn through an overview of foundational ideas such as frames of reference, revelatory examples of time dilation and its attendant principles, an example-based exploration of relativity, and explanations of how and why gravity and spacetime are linked. By demonstrating relativity with practical applications, Styer teaches us to truly understand and appreciate its importance, beauty, and usefulness.

Featuring worked and end-of-chapter problems and illustrated, nontechnical explanations of core concepts, while dotted throughout with questions and answers, puzzles, and paradoxes, "Relativity for the Questioning Mind" is an enjoyable-to-read, complete, concise introduction to one of the most important scientific theories yet discovered. The appendixes provide helpful hints, basic answers to the sample problems, and materials to stimulate further exploration.

A graduate level text on a subject which brings together several areas of mathematics and physics: partial differential equations, differential geometry and general relativity. It explains the basics of the theory of partial differential equations in a form accessible to physicists and the basics of general relativity in a form accessible to mathematicians. In recent years the theory of partial differential equations has come to play an ever more important role in research on general relativity. This is partly due to the growth of the field of numerical relativity, stimulated in turn by work on gravitational wave detection, but also due to an increased interest in general relativity among pure mathematicians working in the areas of partial differential equations and Riemannian geometry, who have realized the exceptional richness of the interactions between geometry and analysis which arise. This book provides the background for those wishing to learn about these topics. It treats key themes in general relativity including matter models and symmetry classes and gives an introduction to relevant aspects of the most important classes of partial differential equations, including ordinary differential equations, and material on functional analysis. These elements are brought together to discuss a variety of important examples in the field of mathematical relativity, including asymptotically flat spacetimes, which are used to describe isolated systems, and spatially compact spacetimes, which are of importance in cosmology.

Ryan Wasserman presents a wide-ranging exploration of puzzles raised by the possibility of time travel, including the grandfather paradox, the bootstrapping paradox, and the twin paradox of special relativity. He draws out their implications for our understanding of time, tense, freedom, fatalism, causation, counterfactuals, laws of nature, persistence, change, and mereology. The Paradoxes of Time Travel is written in an accessible style, and filled with entertaining examples from physics, science fiction, and popular culture.

This book offers a comprehensive, university-level introduction to Einstein's Special Theory of Relativity. In addition to the purely theoretical aspect, emphasis is also given to its historical development as well as to the experiments that preceded the theory and those performed in order to test its validity.The main body of the book consists of chapters on Relativistic Kinematics and Dynamics and their applications, Optics and Electromagnetism. These could be covered in a one-semester course. A more advanced course might include the subjects examined in the other chapters of the book and its appendices.As a textbook, it has some unique characteristics: It provides detailed proofs of the theorems, offers abundant figures and discusses numerous examples. It also includes a number of problems for readers to solve, the complete solutions of which are given at the end of the book.It is primarily intended for use by university students of physics, mathematics and engineering. However, as the mathematics needed is of an upper-intermediate level, the book will also appeal to a more general readership.

In this book, Henry Bar, physicist and the first quantum superhero, guides the reader through the amazing quantum world. His hair-raising adventures in his perilous struggle for quantum coherence are graphically depicted by comics and thoroughly explained to the lay reader. Behind each adventure lies a key concept in quantum physics. These concepts range from the basic quantum coherence and entanglement through tunnelling and the recently discovered quantum decoherence control, to the principles of the emerging technologies of quantum communication and computing. The explanations of the concepts are accessible, but nonetheless rigorous and detailed. They are followed by an account of the broader context of these concepts, their historic perspective, current status and forthcoming developments. Finally, thought-provoking philosophical and cultural implications of these concepts are discussed. The mathematical appendices of all chapters cover in a straightforward manner the core aspects of quantum physics at the level of a university introductory course. The Quantum Matrix presents an entertaining, popular, yet comprehensive picture of quantum physics . It can be read as a light-hearted illustrated tale, a philosophical treatise, or a textbook. Either way, the book lets the reader delve deeply into the wondrous quantum world from diverse perspectives and obtain glimpses into the quantum technologies that are about to reshape our lives. This book offers the reader an enjoyable and rewarding voyage through the quantum world.

From 1900 to 1924 Spain experienced a stage of vigorous academic freedom and unfettered scientific inquiry that strikingly contrasted with the repressive atmosphere of the periods before and after. Thomas Glick explores this "recovery of science" by focusing on the national discussion provoked by Einstein's trip to Spain in 1923. His visit stimulated a debate on the nature and social value of science that was remarkable in a society so recently awakened to the scientific role in the process of modernization. Einstein's universal appeal created the unlikely occasion for a fascination with science that cut across social classes and previously established domains of discourse. The political Right, which in other countries opposed relativity in the name of "traditional" Newtonian science, backed the new theories with surprising enthusiasm. Engineers, a politically conservative group, contributed much of the rank-and-file support for Einstein; physicians, who tended to the Left, also eagerly embraced his ideas, as did a host of mutually antagonistic political groups, including anarcho-syndicalists and bourgeois Catalan nationalists. Professor Glick's analysis of this multidimensional scientific forum provides an unusual amount of information on science in Spain and an opportunity to contrast the Spaniards' reception of Einstein's work and that of other nations during this historical period. Originally published in 1988. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Based on papers presented at the Jerusalem Einstein Centennial Symposium in March 1979, this volume sets forth an articulated sequence of chapters on the impact of Einstein's work, not only in science but in humanistic studies and problems such as international security in the nuclear age. Originally published in 1982. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

This book, explores the conceptual foundations of Einstein's theory of relativity: the fascinating, yet tangled, web of philosophical, mathematical, and physical ideas that is the source of the theory's enduring philosophical interest. Originally published in 1983. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

An in depth exploration of how Clifford algebras and spinors have been sparking collaboration and bridging the gap between Physics and Mathematics. This collaboration has been the consequence of a growing awareness of the importance of algebraic and geometric properties in many physical phenomena, and of the discovery of common ground through various touch points: relating Clifford algebras and the arising geometry to so-called spinors, and to their three definitions (both from the mathematical and physical viewpoint). The main points of contact are the representations of Clifford algebras and the periodicity theorems. Clifford algebras also constitute a highly intuitive formalism, having an intimate relationship to quantum field theory. The text strives to seamlessly combine these various viewpoints and is devoted to a wider audience of both physicists and mathematicians. Among the existing approaches to Clifford algebras and spinors this book is unique in that it provides a didactical presentation of the topic and is accessible to both students and researchers. It emphasizes the formal character and the deep algebraic and geometric completeness, and merges them with the physical applications.

Im Alter von 21 Jahren hat W. Pauli einen Handbuchartikel zur Relativitatstheorie verfasst, der bis heute gelesen und zitiert wird. Er ist wohl der beruhmteste Text zum Thema und wurde nicht zuletzt von A. Einstein begeistert gewurdigt. Die vorliegende Neuausgabe enthalt den Originalartikel sowie weitere, teilweise recht ausfuhrliche Erganzungen, die Pauli im Jahre 1956 fur die englische Ausgabe schrieb. Eine Reihe von Anmerkungen des Herausgebers dienen daruber hinaus als Lesehilfen und zeigen Verbindungen zu modernen Entwicklungen auf."