Das vorliegende Tutorium ART ist die ideale Hilfe und Begleitung zur Vorlesung Allgemeine Relativitatstheorie! Dieses Lehrbuch richtet sich an Studierende, die eine Vorlesung zur ART hoeren, und an alle, die genau wissen wollen, wie die Physik das Zwillingsparadoxon, Schwarze Loecher und die Krummung der Raumzeit beschreibt. Die physikalischen Konzepte der ART, wie Raumzeit oder das AEquivalenzprinzip, werden grundlich motiviert und anschaulich eingefuhrt. Die grundlegenden Begriffe der Differenzialgeometrie, die die mathematische Grundlage der ART darstellen, werden sauber erklart, und mit vielen Beispielen wird dafur gesorgt, dass man mit ihnen sicher und routiniert umgehen kann. Mit diesen Werkzeugen werden dann spannende physikalische Phanomene behandelt: Was passiert, wenn man in ein schwarzes Loch fallt? Was genau passiert mit mir, wenn eine Gravitationswelle durch mich hindurchgeht? Und woher wissen wir, dass es einen Urknall gegeben haben muss? All diese Fragen beantwortet dieses Buch. Das Buch kann als begleitende Lernhilfe parallel zu einer Vorlesung benutzt werden, funktioniert aber auch als Lehrbuch, aus dem man selbststandig die Grundlagen der ART lernen kann. Dabei werden die Lerninhalte nicht nur anschaulich und reich bebildert dargestellt, der Stoff wird auch mit vielen UEbungsaufgaben inklusive ausfuhrlicher Loesungen verfestigt. Der Inhalt Newtonsche Mechanik - Spezielle Relativitatstheorie - Mathematische Grundlagen der SRT - Das AEquivalenzprinzip - Tensorkalkul auf Mannigfaltigkeiten - Geometrie: Metriken und kovariante Ableitungen - Geometrie: Krummung - Die Einsteingleichungen - Symmetrien und Erhaltungssatze - Die Schwarzschildmetrik - Kosmologie - Gravitationswellen

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.

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.

Die bewegte Uhr und eine Uhr im Gravitationsfeld gehen nach. Das beruhmte Paradoxon von den Zwillingen, die sich erst voneinander entfernen und dann wieder zusammenkommen, untersuchen wir zunachst im speziell-relativistischen Gedankenexperiment, also ohne Gravitation. Der Zwilling, der seinen Bruder mit einer hoeheren Geschwindigkeit wieder einholt, bleibt am Ende der jungere, was sich mit der sog. Zwillingsungleichung einfach verifizieren lasst.Die Gravitation kann prinzipiell nicht abgeschirmt werden. Ihren Einfluss auf den Gang einer Uhr verstehen wir mit einem Gedankenexperiment von V. Muller. Wahrend die Zwillinge betragsmassig immer dieselbe Geschwindigkeit zueinander besitzen, gelangen sie aber bei ihrer Bewegung durch den Raum in die Nahe verschiedener Massen, so dass sie unterschiedlicher Gravitation ausgesetzt sind. Das kann dazu fuhren, dass am Ende der zuruckkehrende Zwilling sogar der altere ist.

Every document in "The Collected Papers of Albert Einstein" appears in the language in which it was written, and supplementary paperback volumes present the English translations if all non-English materials. For those desiring a supplement to Volume 5, for instance, this paperback includes translations of correspondence that give a much richer picture of Einstein in his twenties and thirties than we ever had. In addition to illuminating the personal aspects of his life, the letters document his scientific activity: his concentration for years on the unfathomable problems of quanta and radiation, his extensive knowledge of experimental physics, his many fruitful interactions with experimentalists, and finally his long struggle to generalize the 1905 theory of relativity to include gravitation and accelerated frames of reference. This paperback translation does not include notes or annotation of the documentary volume and is not intended for use without the original language documentary edition, which provides the extensive editorial commentary necessary for a full historical and scientific understanding of the documents.

Mit diesem Buch taucht der Leser ein in die exotische Welt der kompakten Sterne. Der Autor ermoeglicht eine verstandliche UEbersicht uber die Entstehung, Eigenschaften und die Physik hinter astrophysikalischen Objekten wie Weisse Zwergen, Neutronensternen oder Schwarzen Loechern. Nach einer Einfuhrung zur Klassifizierung und Entwicklung von Sternen werden die notwendigen Grundlagen von Einsteins Allgemeiner Relativitatstheorie erlautert, die zum Verstandnis benoetigt werden. Anhand von konkreten astrophysikalischen Objekten wird der Leser anschliessend in die Geheimnisse der Gravitation und Physik kompakter Objekte eingefuhrt. Abgerundet wird das Thema mit einem Kapitel zur Entstehung und Detektion von Gravitationswellen, die zurzeit mit advLIGO, advVIRGO und KAGRA sehr erfolgreich detektiert werden. Der Leser erhalt Antworten auf spannende Fragen wie: Wie sollen wir uns einen Weissen Zwerg oder gar ein Schwarzes Loch vorstellen? Was bedeutet die Chandrasekhar Masse? Gibt es Schwarze Loecher wirklich in unserem Universum? Welche Bedeutung hat die Relativitatstheorie auf diesem Gebiet? Was sind Gravitationswellen? Wie entstehen Gravitationswellen beim Verschmelzen von kompakten Objekten? Wie kann man diese Wellen nachweisen? Dieses Buch eignet sich durch seine Verknupfung von Astronomie und Physik sehr gut fur Bachelor- und Masterausbildung in Physik und Astronomie, aber auch interessierte Laien koennen hier einen Einstieg in das Thema finden. Mit diesem Buch soll auch ein Beitrag zur Wurdigung der Leistung Albert Einsteins vor uber 100 Jahren geleistet werden, ohne dessen Allgemeine Relativitatstheorie das Verstandnis von kompakten Objekten nicht moeglich gewesen ware.

Eleven most important original papers on special and general theories. Seven by Einstein, two by Lorentz, one each by Minkowski and Weyl.

Gamma-ray bursts (GRBs) are the most luminous explosions in the universe, which within seconds release energy comparable to what the Sun releases in its entire lifetime. The field of GRBs has developed rapidly and matured over the past decades. Written by a leading researcher, this text presents a thorough treatment of every aspect of the physics of GRBs. It starts with an overview of the field and an introduction to GRB phenomenology. After laying out the basics of relativity, relativistic shocks, and leptonic and hadronic radiation processes, the volume covers all topics related to GRBs, including a general theoretical framework, afterglow and prompt emission models, progenitor, central engine, multi-messenger aspects (cosmic rays, neutrinos, and gravitational waves), cosmological connections, and broader impacts on fundamental physics and astrobiology. It is suitable for advanced undergraduates, graduate students, and experienced researchers in the field of GRBs and high-energy astrophysics in general.

Ross P. Cameron argues that the flow of time is a genuine feature of reality. He suggests that the best version of the A-Theory is a version of the Moving Spotlight view, according to which past and future beings are real, but there is nonetheless an objectively privileged present. Cameron argues that the Moving Spotlight theory should be viewed as having more in common with Presentism (the view that reality is limited to the present) than with the B-Theory (the view that time is just another dimension like space through which things are spread out). The Moving Spotlight view, on this picture, agrees with Presentism that everything is the way it is now, it simply thinks that non-present beings are amongst the things that are now some way. Cameron argues that the Moving Spotlight theory provides the best account of truthmakers for claims about what was or will be the case, and he defends the view against a number of objections, including McTaggart's argument that the A-Theory is inconsistent, and the charge that if the A-Theory is true but presentism false then we could not know that we are present. The Moving Spotlight defends an account of the open future-that what will happen is, as yet, undetermined-Land argues that this is a better account than that available to the Growing Block theory.

CHOSEN AS A BOOK OF THE YEAR BY THE GUARDIAN, DAILY TELEGRAPH, NEW STATESMAN AND BBC SCIENCE FOCUS 'An intimate, unique, and inspiring perspective on the life and work of one of the greatest minds of our time. Filled with insight, humour, and never-before-told stories, it's a view of Stephen Hawking that few have seen and all will appreciate' James Clear, author of Atomic Habits An icon of the last fifty years, Stephen Hawking seems to encapsulate genius: not since Albert Einstein has a scientific figure held such a position in popular consciousness. In this enthralling memoir, writer and physicist Leonard Mlodinow tells the story of his friend and their collaboration, offering an intimate account of this giant of science. The two met in 2003, when Stephen asked Leonard if he would consider writing a book with him, the follow up to the bestselling A Brief History of Time. As they spent years working on a second book, The Grand Design, they forged a deep connection and Leonard gained a much better understanding of Stephen's daily life and struggles -- as well as his compassion and good humour. Together they obsessed over the perfect sentence, debated the physics, and occasionally punted on Cambridge's waterways with champagne and strawberries. In time, Leonard was able to finish Stephen's jokes, chide his sporadic mischief, and learn how the hardships of his illness helped forge that unique perspective on the universe. By weaving together their shared story with a clear-sighted portrayal of Hawking's scientific achievements, Mlodinow creates a beautiful portrait of Stephen Hawking as a brilliant, impish and generous man whose life was not only exceptional but also genuinely inspiring.

Was sind die Einsteingleichungen? Kann man sie verstehen, ohne Physik studiert zu haben? Dieses Buch gibt die Antwort: Behutsam und detailreich gibt der Autor naturwissenschaftlich Interessierten einen verstandlichen Zugang zu Einsteins Relativitatstheorien. An Vorkenntnissen wird nur das vorausgesetzt, was man in der Oberstufe im Gymnasium lernt. Leser setzen sich mit den physikalischen Phanomenen und mathematischen Techniken auseinander, damit sie Einsteins Gravitationstheorie auch quantitativ verstehen koennen. Leser nahern sich somit Antworten auf Fragen rund um die Allgemeine Relativitatstheorie: Was unterscheidet Einsteins und Newtons Gravitationstheorie? Wie kann man gravitative Anziehung geometrisch beschreiben? Wie kann ein Schwarzes Loch Licht "verschlucken"?

This monograph describes the different formulations of Einstein's General Theory of Relativity. Unlike traditional treatments, Cartan's geometry of fibre bundles and differential forms is placed at the forefront, and a detailed review of the relevant differential geometry is presented. Particular emphasis is given to general relativity in 4D space-time, in which the concepts of chirality and self-duality begin to play a key role. Associated chiral formulations are catalogued, and shown to lead to many practical simplifications. The book develops the chiral gravitational perturbation theory, in which the spinor formalism plays a central role. The book also presents in detail the twistor description of gravity, as well as its generalisation based on geometry of 3-forms in seven dimensions. Giving valuable insight into the very nature of gravity, this book joins our highly prestigious Cambridge Monographs in Mathematical Physics series. It will interest graduate students and researchers in the fields of theoretical physics and differential geometry.

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.

Have you ever wondered about Time: what it is or how to discuss it? If you have, then you may have been bewildered by the many different views and opinions in many diverse fields to be found, such as physics, mathematics, philosophy, religion, history, and science fiction novels and films. This book will help you unravel fact from fiction. It provides a broad survey of many of these views, these images of time, covering historical, cultural, philosophical, biological, mathematical and physical images of time, including classical and quantum mechanics, special and general relativity and cosmology. This book gives you more than just a review of such images. It provides the reader a basis for judging the scientific soundness of these various images. It develops the reader's critical ability to distinguish Images of Time in terms of its contextual completeness. Differentiating between metaphysical images (which cannot be scientifically validated) and those that could, in principle, be put to empirical test. Showing that mathematical and classical mechanical images are more complete, and genuine quantum mechanics based images have the greatest degree of contextual completeness. Through the use of a simple algorithm, the reader can decide the classification of any of the images of time discussed in this book. These distinctions are of particular importance in this day and age, when we are flooded by a plethora of competing Images of Time. Many of these have no scientific basis or empirical support or content. This book will be of value not only to philosophers, scientists and students, but also to the general reader interested in this fundamental topic, because it introduces a method of distinguishing between science fiction and science fact.

Dieses Buch bietet eine Einfuhrung in die spezielle und allgemeine Relativitatstheorie fur Physiker, Ingenieure und andere Naturwissenschaftler, die einen Einstieg in das Thema suchen, ohne sich in zu viel neue Mathematik einzuarbeiten. Einsteins grundlegende Gleichungen werden so ohne die Hilfe von Tensoren das erste Mal nur mit Hilfe der Matrizenalgebra hergeleitet. Im 1. Kapitel wird die spezielle und im 2. Kapitel die allgemeine Relativitatstheorie behandelt. Die Schwarzschildloesung fur eine kugelfoermige Masse wird im 3. Kapitel angegeben, sowie "Schwarze Loecher" vorgestellt und untersucht. Noch erforderliche Mathematik wird entweder direkt oder im Anhang zur Verfugung gestellt.

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

Ross P. Cameron argues that the flow of time is a genuine feature of reality. He suggests that the best version of the A-Theory is a version of the Moving Spotlight view, according to which past and future beings are real, but there is nonetheless an objectively privileged present. Cameron argues that the Moving Spotlight theory should be viewed as having more in common with Presentism (the view that reality is limited to the present) than with the B-Theory (the view that time is just another dimension like space through which things are spread out). The Moving Spotlight view, on this picture, agrees with Presentism that everything is the way it is now, it simply thinks that non-present beings are amongst the things that are now some way. Cameron argues that the Moving Spotlight theory provides the best account of truthmakers for claims about what was or will be the case, and he defends the view against a number of objections, including McTaggart's argument that the A-Theory is inconsistent, and the charge that if the A-Theory is true but presentism false then we could not know that we are present. The Moving Spotlight defends an account of the open future-that what will happen is, as yet, undetermined-and argues that this is a better account than that available to the Growing Block theory.

Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a 'black hole' in space; and secondly, that there will exist singularities in space-time itself.

These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large.

Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions.

These conditions are shown to be satisfied in the vicinity of stars of more than twice the solar mass near the endpoint of their nuclear evolution, and in a time-reversed sense for the universe as a whole. In the first case, the singularity in our past. A discussion of the Cauchy problem for General Relativity is also included in the book.

This advanced undergraduate text introduces Einstein's general theory of relativity. The topics covered include geometric formulation of special relativity, the principle of equivalence, Einstein's field equation and its spherical-symmetric solution, as well as cosmology. An emphasis is placed on physical examples and simple applications without the full tensor apparatus. It begins by examining the physics of the equivalence principle and looks at how it inspired Einstein's idea of curved spacetime as the gravitational field. At a more mathematically accessible level, it provides a metric description of a warped space, allowing the reader to study many interesting phenomena such as gravitational time dilation, GPS operation, light deflection, precession of Mercury's perihelion, and black holes. Numerous modern topics in cosmology are discussed from primordial inflation and cosmic microwave background to the dark energy that propels an accelerating universe. Building on Cheng's previous book, 'Relativity, Gravitation and Cosmology: A Basic Introduction', this text has been tailored to the advanced student. It concentrates on the core elements of the subject making it suitable for a one-semester course at the undergraduate level. It can also serve as an accessible introduction of general relativity and cosmology for those readers who want to study the subject on their own. The proper tensor formulation of Einstein's field equation is presented in an appendix chapter for those wishing to glimpse further at the mathematical details.

In recent years, the old idea that gauge theories and string theories are equivalent has been implemented and developed in various ways, and there are by now various models where the string theory / gauge theory correspondence is at work. One of the most important examples of this correspondence relates Chern-Simons theory, a topological gauge theory in three dimensions which describes knot and three-manifold invariants, to topological string theory, which is deeply related to Gromov-Witten invariants. This has led to some surprising relations between three-manifold geometry and enumerative geometry. This book gives the first coherent presentation of this and other related topics. After an introduction to matrix models and Chern-Simons theory, the book describes in detail the topological string theories that correspond to these gauge theories and develops the mathematical implications of this duality for the enumerative geometry of Calabi-Yau manifolds and knot theory. It is written in a pedagogical style and will be useful reading for graduate students and researchers in both mathematics and physics willing to learn about these developments.

With this reader-friendly book, it doesn't take an Einstein to understand the theory of relativity and its remarkable consequences.

In clear, understandable terms, physicist Richard Wolfson explores the ideas at the heart of relativity and shows how they lead to such seeming absurdities as time travel, curved space, black holes, and new meaning for the idea of past and future. Drawing from years of teaching modern physics to nonscientists, Wolfson explains in a lively, conversational style the simple principles underlying Einstein's theory.

Relativity, Wolfson shows, gave us a new view of space and time, opening the door to questions about their flexible nature: Is the universe finite or infinite? Will it expand forever or eventually collapse in a "big crunch"? Is time travel possible? What goes on inside a black hole? How does gravity really work? These questions at the forefront of twenty-first-century physics are all rooted in the profound and sweeping vision of Albert Einstein's early twentieth-century theory. Wolfson leads his readers on an intellectual journey that culminates in a universe made almost unimaginably rich by the principles that Einstein first discovered.

"Wolfson takes the fear out of Einstein's relativity theory in this brisk piece of pop-science."—Publishers Weekly

"In a clear style, [Wolfson] spreads before his readers the historical and conceptual background of [relativity] theory, emphasizing its simplicity at every opportunity. He also offers beautifully clear explanations of such classic puzzles as the Twin Paradox. A strong overview for the lay reader."—Library Journal

"Wolfson explains in a lively, conversational style the simple priciples underlying Einstein's theory."—Astronomical Society of the Pacific

"Wolfson's account is head and shoulders above most, and is a good place to start out."—New Scientist

"With straightforward language and clear examples, Wolfson proves you don't have to be an Einstein to understand his great ideas."—Science News

"Wolfson leads the reader gently and irresistibly down the logical path that Einstein followed to arrive at his theories."—Washington Post Book World

What does the passage of time consist in? There are some suggestive metaphors. aEvents approach us, pass us, and recede from us, like sticks and leaves floating on the river of time.a aWe are moving from the past into the future, like ships sailing into an unknown ocean.a There is surely something right and deep about these metaphors. But how close are they to the literal truth? In this book Bradford Skow argues that they are far from the literal truth. Skowas argument takes the form of a defense of the block universe theory of time, a theory that, in many ways, treats time as a dimension of reality that closely resembles the three dimensions of space. Opposed to the block universe theory of time are theories that take the metaphors more seriously: presentism, the moving spotlight theory, the growing block theory, and the branching time theory. These are theories of arobusta passage of time, or aobjective becoming.a Skow argues that the best of these theories, the block universe theoryas most worthy opponent, is the moving spotlight theory, the theory that says that apresentnessa moves along the series of times from the past into the future. Skow defends the moving spotlight theory against the objection that it is inconsistent, and the objection that it cannot answer the question of how fast time passes. He also defends it against the objection that it is incompatible with Einsteinas theory of relativity. Skow proposes several ways in which the moving spotlight theory may be made compatible with the theory of relativity. Still, this book is ultimately a defense of the block universe theory, not of the moving spotlight theory. Skow holds that the best arguments against the block universe theory, and for the moving spotlight theory, start from the idea that, somehow, the passage of time is given to us in experience. Skow discusses several different arguments that start from this idea, and argues that they all fail.