Starting with the idea of an event and finishing with a description of the standard big-bang model of the Universe, this textbook provides a clear, concise and up-to-date introduction to the theory of general relativity, suitable for final-year undergraduate mathematics or physics students. Throughout, the emphasis is on the geometric structure of spacetime, rather than the traditional coordinate-dependent approach. This allows the theory to be pared down and presented in its simplest and most elegant form. Topics covered include flat spacetime (special relativity), Maxwell fields, the energy-momentum tensor, spacetime curvature and gravity, Schwarzschild and Kerr spacetimes, black holes and singularities, and cosmology. In developing the theory, all physical assumptions are clearly spelled out and the necessary mathematics is developed along with the physics. Exercises are provided at the end of each chapter and key ideas in the text are illustrated with worked examples. Solutions and hints to selected problems are also provided at the end of the book. This textbook will enable the student to develop a sound understanding of the theory of general relativity, and all the necessary mathematical machinery.

The Theory of Special Relativity is one of the most profound discoveries of the twentieth century. Einstein's Mirror blends a simple, nonmathematical account of the theory of special relativity and gravitation with a description of the way experiments have triumphantly supported these theories. The authors explore the many applications of relativity in atomic and nuclear physics, which are many and range from satellite navigation systems, particle accelerators and nuclear power to quantum chemistry, antimatter and black holes. The book also features a superb collection of photographs and includes amusing anecdotes and biographies about the early pioneers. In the closing chapter, the authors examine the influence of Einstein's relativity on the development of science fiction. General readers with an interest in science will enjoy and benefit from this fascinating and accessible introduction to one of the most important areas of physics.

Gitter messen, wenn WH dafUr ausschlieBlich geometrische Gebilde verwenden, wel che in diesem Gitter auch physikalisch existieren? Physikalische Objekte, die dafUr in Frage kommen, sind Versetzungen, welche in jedem Kristall in einer ungeheuer groBen Zahl vorhanden sind. Wir suchen dann einmal nach solchen, physikalisch stabilen Formen dieser Versetzungen, die geeignet sind, uns ein MaB fUr eine Lange zu liefern, sowie Ferner nach physikalisch stabilen, schwingenden Versetzungen, die uns eine Schwingungsdauer fUr eine Uhr hergeben. Dies gelingt mit einer sehr ge nau untersuchten Gleichung fUr Versetzungen in Kristallen, mit der sog. sine Gordon - Gleichung, fUr die wir eine denkbar einfache physikalische BegrUndung angeben konnen. Darauf aufbauend werden wir dann einen relativistischen Effekt nach dem andern entdecken, am Ende auch das Prinzip von der universellen Konstanz einer ausgezeichneten Signalgeschwindigkeit, welche hier auf dem Gitter definiert ist: Die Kontinuumsnaherung eines Kristallgitters wird als Modell einer relativistischen Raum - Zeit erkennbar. Die Grundidee, die zu dieser Reduktion der relativistischen Phanomene auf be grifflich leichter faBbare Aussagen fuhrt, laBt sich kurz so formulieren: FUr die physikalischen Konstituenten eines idealen Raumgitters postulieren wir die Axio matik der Newtonschen Mechanik. Aber erst die auf diesem Gitter existierenden, lokalen Abweichungen von der idealen Struktur (Konfigurationen von Versetzun gen im KristaII) besitzen in bezug auf dieses Gitter diejenigen tragen Massen, deren Bewegung wir beobachten und fUr deren Bewegung wir dann - innerhalb relativ leicht Uberschaubarer GUltigkeitsgrenzen - die Gesetze der SpezieIIen Relativitats theorie finden."

This book is an introduction to gravitational waves and related astrophysics. It provides a bridge across the range of astronomy, physics and cosmology that comes into play when trying to understand the gravitational-wave sky. Starting with Einstein's theory of gravity, chapters develop the key ideas step by step, leading up to the technology that finally caught these faint whispers from the distant universe. The second part of the book makes a direct connection with current research, introducing the relevant language and making the involved concepts less mysterious. The book is intended to work as a platform, low enough that anyone with an elementary understanding of gravitational waves can scramble onto it, but at the same time high enough to connect readers with active research - and the many exciting discoveries that are happening right now. The first part of the book introduces the key ideas, following a general overview chapter and including a brief reminder of Einstein's theory. This part can be taught as a self-contained one semester course. The second part of the book is written to work as a collection of "set pieces" with core material that can be adapted to specific lectures and additional material that provide context and depth. A range of readers may find this book useful, including graduate students, astronomers looking for basic understanding of the gravitational-wave window to the universe, researchers analysing data from gravitational-wave detectors, and nuclear and particle physicists.

Enjoy Our Universe is a guide for an enjoyable visit to the Universe. The "Universe" refers to all "observable things," ranging in size from the entire cosmos to elementary particles. This small tome on fundamental physics, cosmology, Higgs bosons, time travel and all that, is unlike any other analogous book. Its scientific statements are correct or, at least, they coincide with the opinions held by the vast majority of experts. It establishes clear distinctions between things we know for sure - in the sense of having strong observational support for them - and things that we know that we do not know, or we do not understand. In this sense, it is scientifically honest. In descriptions of our Universe and of the way it functions, beauty is a recurring word. In an attempt to portray its beauty from the eyes of the beholder, the book is profusely illustrated. Its offbeat, tongue-in-cheek illustrations greatly enhance its readability, particularly in those chapters whose understanding, admittedly, requires a little extra effort. This book's idiosyncracies remind us of our own smallness and eccentricities even as we read about the logic, function and magnificence of the Universe.

This text is more conceptually and mathematically than experimentally orientated, elaborating on the underlying logic and dwelling on the subtleties and apparent paradoxes. In this updated edition additional examples and problems have been included.

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.

Die Sprache und die Methoden der modernen Differentialgeometrie sind in der vergangenen Dekade immer mehr in die theoretische Physik eingedrungen. Was vor 15 Jahren, als das Buch zuerst als Vorlesungsskriptum herauskam, noch extravagant erschien, ist heute ein Gemeinplatz. Dies hat mich in der Ansicht gestarkt, dass die Studenten der theoretischen Physik diese Sprache lernen mussen, je eher desto besser. Schliesslich werden sie die Professoren des 21. Jahrhunderts sein und es ware absurd, wurden sie dann die Mathematik des 19. Jahrhunderts lehren. Daher habe ich in der neuen Auflage auf dieser Symbolik beharrt, einige Fehler korrigiert und ein Kapi- tel uber Eichtheorien hinzugefugt. Da es sich gezeigt hat, dass sie die fundamentalen Wechselwirkungen beschreiben und ihre Struktur zumindest auf dem klassischen Ni- veau hinreichend klar ist, scheinen sie mir zur Minimalausrustung zu gehoeren, uber die jeder Theoretiker verfugen muss. Mit Bedauern musste ich davon Abstand nehmen, die neueren Entwicklungen der Kosmologie und Kaluza-Klein-artige Theorien aufzu- nehmen, aber ich fuhlte mich an mein ursprungliches Versprechen gebunden, den Studenten keine theoretischen Spekulationen aufzuburden, fur die es keine sichere experimentelle Evidenz gibt. Vielen Physikern bin ich fur Hinweise bezuglich dieses Bandes sehr verpflichtet. Insbesondere P. Aichelburg, H. Rumpf und vor allem H. Urbantke haben zahlreiche Korrekturen und Verbesserungen angebracht. I. Dahl-Jensen sei dafur gedankt, dass sie manche nach Gefuhl angefertigte Zeichnungen mit dem Computer ins richtige Lot gebracht hat.

In den letzten Dekaden hat das Gebiet der klassischen dynamischen Systeme eine beachtliche Renaissance erlebt, und manches, was beim erst en Erscheinen dieses Kur- ses als mathematisch zu hochgestochen erschien, ist heute Gemeingut der aktiven Physiker geworden. Das Ziel der Neuauflage ist es, . dieser Entwicklung zu dienen, indem ich versucht habe, das Buch leserfreundlicher zu gestalten und Fehler auszu- merzen. Da schon die erste Auflage ffir eine einsemestrige Vorlesung reichlich beladen war, wurde neues Material nur in dem Mafie aufgenommen, als anderes weggelassen oder vereinfacht werden konnte. Eine Erweiterung muf3te jedoch das Kapitel mit dem Be- weis des KAM-Satzes erfahren, urn dem neuen Trend in der Physik Rechnung zu tragen. Dieser besteht nicht nur in der Verwendung feinerer mathematischer Hilfs- mittel, sondern auch in einer Neubewertung des Wortes "fundamental". Was frfiher als Schmutzeffekt abgetan wurde, erscheint heute als Folge eines tieferen Prinzips. Ja so- gar diese Keplerschen Gesetze, welche die Radien der Planetenbahnen bestimmen und die man als mystischen Unsinn gerne verschwieg, scheinen in Richtung einer Wahrheit zu deuten, die sich oberflachlicher Betrachtung verschlief3t: SchachteluI). g vollkomme- ner platonischer Korper ffihrt zu Verhaltnissen von Radien, die irrational sind, aber algebraischen Gleichungen niederer Ordnung genfigen. Gerade solche Irrationalzahlen lassen sich am schlechtesten durch rationale approximieren, und Bahnen mit diesem Radiusverhaltnis sind gegenfiber gegenseitigen Storungen am robustesten, da sie am wenigsten unter Resonanzeffekten leiden. In letzter Zeit wurden einige fiberraschende Resultate fiber chaotische Systeme gefunden, doch hat ten deren Beweise leider den Rahmen dieses Buches gesprengt und muf3ten unterbleiben.

Classical electromagnetism - one of the fundamental pillars of physics - is an important topic for all types of physicists from the theoretical to the applied. The subject is widely recognized to be one of the most challenging areas of the physics curriculum, both for students to learn and for lecturers to teach. Although textbooks on electromagnetism are plentiful, hardly any are written in the question-and-answer style format adopted in this book. It contains nearly 300 worked questions and solutions in classical electromagnetism, and is based on material usually encountered during the course of a standard university physics degree. Topics covered include some of the background mathematical techniques, electrostatics, magnetostatics, elementary circuit theory, electrodynamics, electromagnetic waves and electromagnetic radiation. For the most part the book deals with the microscopic theory, although we also introduce the important subject of macroscopic electromagnetism as well. Nearly all questions end with a series of comments whose purpose is to stimulate inductive reasoning and reach various important conclusions arising from the problem. Occasionally, points of historical interest are also mentioned. Both analytical and numerical techniques are used in obtaining and analyzing solutions. All computer calculations are performed with MathematicaCO (R) and the relevant code is provided in a notebook; either in the solution or the comments.

E=mc2 is the world's most famous equation. Discover the thought process and physics behind general relativity and Einstein's contribution to science, in this authorized edition. In this collection of his seven most important essays on physics, Einstein guides his reader step-by-step through the many layers of scientific theory that formed a starting point for his discoveries. By both supporting and refuting the theories and scientific efforts of his predecessors, Einstein reveals in a clear voice the origins and meaning of such significant topics as physics and reality, the fundamentals of theoretical physics, the common language of science, the laws of science and of ethics, and an elementary derivation of the equivalence of mass and energy. This remarkable collection allows the general reader to understand not only the significance of Einstein's masterpiece, but also the brilliant mind behind it. This authorized book features a new introduction by Neil Berger and an illustrated biography of Albert Einstein, which includes rare photos and never-before-seen documents from the Albert Einstein Archives at the Hebrew University of Jerusalem.

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

Einstein's standard and battle-tested geometric theory of gravity--spacetime tells mass how to move and mass tells spacetime how to curve--is expounded in this book by Ignazio Ciufolini and John Wheeler. They give special attention to the theory's observational checks and to two of its consequences: the predicted existence of gravitomagnetism and the origin of inertia (local inertial frames) in Einstein's general relativity: inertia "here" arises from mass "there."

The authors explain the modern understanding of the link between gravitation and inertia in Einstein's theory, from the origin of inertia in some cosmological models of the universe, to the interpretation of the initial value formulation of Einstein's standard geometrodynamics; and from the devices and the methods used to determine the local inertial frames of reference, to the experiments used to detect and measure the "dragging of inertial frames of reference." In this book, Ciufolini and Wheeler emphasize present, past, and proposed tests of gravitational interaction, metric theories, and general relativity. They describe the numerous confirmations of the foundations of geometrodynamics and some proposed experiments, including space missions, to test some of its fundamental predictions--in particular gravitomagnetic field or "dragging of inertial frames" and gravitational waves.

Somewhere near the heart of existence, shimmers the ethereal beauty of the mystery of Time. Though seemingly familiar to us all, time harbours secrets that penetrate the very deepest levels of reality, and though we feel certain in our conviction that we're swept forth upon the crest of its never-ending flow, with Einstein's discovery of relativity came what is perhaps the most stunning realisation in the entire history of scientific thought - the wondrously breathtaking revelation that in reality, there's actually no such thing as the passage of time... How can this extraordinary truth be reconciled with the reality we so surely suppose to experience? What does it mean for the very human concerns of life and death, free will, identity, and self? What should it mean for our philosophy? And how should it inform our world view? The search for answers leads through the fantastical realm of quantum physics, and the strange parallel worlds it describes, as we discover that the answers which such questions provoke, are perhaps even more profound than the questions themselves. Buried deep within the riddle of time, lies the staggering beauty of the world. As we peel back the layers to try and sneak a glimpse into eternity, we find a light shining not only upon the nature of reality, but on the nature of ourselves...

These two volumes are the proceedings of a major International Symposium on General Relativity held at the University of Maryland in March 1993 to celebrate the sixtieth birthdays of Professor Charles Misner and Professor Dieter Brill. The volumes cover classical general relativity, quantum gravity and quantum cosmology, canonical formulation and the initial value problem, topology and geometry of spacetime and fields, mathematical and physical cosmology, and black hole physics and astrophysics. As invited articles, the papers in these volumes have an aim which goes beyond that of a standard conference proceedings. Not only do the authors discuss the most recent research results in their fields, but many also provide historical perspectives on how the subjects have developed and offer individual insights in their search for new directions.