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| problem book in relativity and gravitation: Problem Book in Relativity and Gravitation Alan P Lightman, William H. Press, Richard H. Price, Saul A. Teukolsky, 2017-09-01 An essential resource for learning about general relativity and much more, from four leading experts Important and useful to every student of relativity, this book is a unique collection of some 475 problems--with solutions--in the fields of special and general relativity, gravitation, relativistic astrophysics, and cosmology. The problems are expressed in broad physical terms to enhance their pertinence to readers with diverse backgrounds. In their solutions, the authors have attempted to convey a mode of approach to these kinds of problems, revealing procedures that can reduce the labor of calculations while avoiding the pitfall of too much or too powerful formalism. Although well suited for individual use, the volume may also be used with one of the modem textbooks in general relativity. |
| problem book in relativity and gravitation: Gravitation Charles W. Misner, Kip S. Thorne, John Archibald Wheeler, 2017-10-24 Spacetime physics -- Physics in flat spacetime -- The mathematics of curved spacetime -- Einstein's geometric theory of gravity -- Relativistic stars -- The universe -- Gravitational collapse and black holes -- Gravitational waves -- Experimental tests of general relativity -- Frontiers |
| problem book in relativity and gravitation: Relativity and Gravitation Jiří Bičák, Tomáš Ledvinka, 2014-06-06 In early April 1911 Albert Einstein arrived in Prague to become full professor of theoretical physics at the German part of Charles University. It was there, for the first time, that he concentrated primarily on the problem of gravitation. Before he left Prague in July 1912 he had submitted the paper “Relativität und Gravitation: Erwiderung auf eine Bemerkung von M. Abraham” in which he remarkably anticipated what a future theory of gravity should look like. At the occasion of the Einstein-in-Prague centenary an international meeting was organized under a title inspired by Einstein's last paper from the Prague period: Relativity and Gravitation, 100 Years after Einstein in Prague. The main topics of the conference included: classical relativity, numerical relativity, relativistic astrophysics and cosmology, quantum gravity, experimental aspects of gravitation and conceptual and historical issues. The conference attracted over 200 scientists from 31 countries, among them a number of leading experts in the field of general relativity and its applications. This volume includes abstracts of the plenary talks and full texts of contributed talks and articles based on the posters presented at the conference. These describe primarily original results of the authors. Full texts of the plenary talks are included in the volume General Relativity, Cosmology and Astrophysics--Perspectives 100 Years after Einstein in Prague, eds. J. Bičák and T. Ledvinka, published also by Springer Verlag. |
| problem book in relativity and gravitation: Gravity James B. Hartle, 2021-06-24 Einstein's theory of general relativity is a cornerstone of modern physics. It also touches upon a wealth of topics that students find fascinating – black holes, warped spacetime, gravitational waves, and cosmology. Now reissued by Cambridge University Press, this ground-breaking text helped to bring general relativity into the undergraduate curriculum, making it accessible to virtually all physics majors. One of the pioneers of the 'physics-first' approach to the subject, renowned relativist James B. Hartle, recognized that there is typically not enough time in a short introductory course for the traditional, mathematics-first, approach. In this text, he provides a fluent and accessible physics-first introduction to general relativity that begins with the essential physical applications and uses a minimum of new mathematics. This market-leading text is ideal for a one-semester course for undergraduates, with only introductory mechanics as a prerequisite. |
| problem book in relativity and gravitation: Relativity, Gravitation and Cosmology Ta-Pei Cheng, 2010 An introduction to Einstein's general theory of relativity, this work is structured so that interesting applications, such as gravitational lensing, black holes and cosmology, can be presented without the readers having to first learn the difficult mathematics of tensor calculus. |
| problem book in relativity and gravitation: Introduction to General Relativity Cosimo Bambi, 2018-06-18 Following the approach of Lev Landau and Evgenii Lifshitz, this book introduces the theory of special and general relativity with the Lagrangian formalism and the principle of least action. This method allows the complete theory to be constructed starting from a small number of assumptions, and is the most natural approach in modern theoretical physics. The book begins by reviewing Newtonian mechanics and Newtonian gravity with the Lagrangian formalism and the principle of least action, and then moves to special and general relativity. Most calculations are presented step by step, as is done on the board in class. The book covers recent advances in gravitational wave astronomy and provides a general overview of current lines of research in gravity. It also includes numerous examples and problems in each chapter. |
| problem book in relativity and gravitation: Topics in the Foundations of General Relativity and Newtonian Gravitation Theory David B. Malament, 2012-04-02 In Topics in the Foundations of General Relativity and Newtonian Gravitation Theory, David B. Malament presents the basic logical-mathematical structure of general relativity and considers a number of special topics concerning the foundations of general relativity and its relation to Newtonian gravitation theory. These special topics include the geometrized formulation of Newtonian theory (also known as Newton-Cartan theory), the concept of rotation in general relativity, and Gödel spacetime. One of the highlights of the book is a no-go theorem that can be understood to show that there is no criterion of orbital rotation in general relativity that fully answers to our classical intuitions. Topics is intended for both students and researchers in mathematical physics and philosophy of science. |
| problem book in relativity and gravitation: A First Course in General Relativity Bernard Schutz, 2009-05-14 Second edition of a widely-used textbook providing the first step into general relativity for undergraduate students with minimal mathematical background. |
| problem book in relativity and gravitation: 300 Problems in Special and General Relativity Mattias Blennow, Tommy Ohlsson, 2021-12-09 Einstein's theories of special relativity and general relativity form a core part of today's undergraduate (or Masters-level) physics curriculum. This is a supplementary problem book or student's manual, consisting of 150 problems in each of special and general relativity. The problems, which have been developed, tested and refined by the authors over the past two decades, are a mixture of short-form and multi-part extended problems, with hints provided where appropriate. Complete solutions are elaborated for every problem, in a different section of the book; some solutions include brief discussions on their physical or historical significance. Designed as a companion text to complement a main relativity textbook, it does not assume access to any specific textbook. This is a helpful resource for advanced students, for self-study, a source of problems for university teaching assistants, or as inspiration for instructors and examiners constructing problems for their lectures, homework or exams. |
| problem book in relativity and gravitation: General Relativity Hans Stephani, 1990-06-29 This book is an excellent introduction to the subjects of gravitation and space-time structure. It presumes a good background in special relativity, electrodynamics, and classical mechanics. The book discusses the foundations of Riemannian geometry; the derivation of the Einstein field equations; linearised theory, far fields and gravitational waves; the invariant characterization of exact solutions; gravitational collapse; cosmology; and a final chapter deals with alternative gravitation theories and the problem of quantum gravity. This revised and correct edition brings the experimental evidence up to date. In addition, the sections on quantum gravity have been rewritten and enlarged, and now form a coherent introduction to this subject. |
| problem book in relativity and gravitation: Gravitational Curvature Theodore Frankel, 2013-04-10 This classic text and reference monograph applies modern differential geometry to general relativity. A brief mathematical introduction to gravitational curvature, it emphasizes the subject's geometric essence and stresses the global aspects of cosmology. Suitable for independent study as well as for courses in differential geometry, relativity, and cosmology. 1979 edition. |
| problem book in relativity and gravitation: Relativity Visualized , 1985 Perfect for those interested in physics but who are not physicists or mathematicians, this book makes relativity so simple that a child can understand it. By replacing equations with diagrams, the book allows non-specialist readers to fully understand the concepts in relativity without the slow, painful progress so often associated with a complicated scientific subject. It allows readers not only to know how relativity works, but also to intuitively understand it. |
| problem book in relativity and gravitation: Gravitation T. Padmanabhan, 2015-12-01 Covering all aspects of gravitation in a contemporary style, this advanced textbook is ideal for graduate students and researchers in all areas of theoretical physics. The AoFoundationAo section develops the formalism in six chapters, and uses it in the next four chapters to discuss four key applications - spherical spacetimes, black holes, gravitational waves and cosmology. The six chapters in the AoFrontierAo section describe cosmological perturbation theory, quantum fields in curved spacetime, and the Hamiltonian structure of general relativity, among several other advanced topics, some of which are covered in-depth for the first time in a textbook. The modular structure of the book allows different sections to be combined to suit a variety of courses. Over 200 exercises are included to test and develop the readerAos understanding. There are also over 30 projects, which help readers make the transition from the book to their own original research. |
| problem book in relativity and gravitation: General Relativity Robert M. Wald, 1984-06-15 Wald's book is clearly the first textbook on general relativity with a totally modern point of view; and it succeeds very well where others are only partially successful. The book includes full discussions of many problems of current interest which are not treated in any extant book, and all these matters are considered with perception and understanding.—S. Chandrasekhar A tour de force: lucid, straightforward, mathematically rigorous, exacting in the analysis of the theory in its physical aspect.—L. P. Hughston, Times Higher Education Supplement Truly excellent. . . . A sophisticated text of manageable size that will probably be read by every student of relativity, astrophysics, and field theory for years to come.—James W. York, Physics Today |
| problem book in relativity and gravitation: The Problem of Time Edward Anderson, 2017-09-18 This book is a treatise on time and on background independence in physics. It first considers how time is conceived of in each accepted paradigm of physics: Newtonian, special relativity, quantum mechanics (QM) and general relativity (GR). Substantial differences are moreover uncovered between what is meant by time in QM and in GR. These differences jointly source the Problem of Time: Nine interlinked facets which arise upon attempting concurrent treatment of the QM and GR paradigms, as is required in particular for a background independent theory of quantum gravity. A sizeable proportion of current quantum gravity programs - e.g. geometrodynamical and loop quantum gravity approaches to quantum GR, quantum cosmology, supergravity and M-theory - are background independent in this sense. This book's foundational topic is thus furthermore of practical relevance in the ongoing development of quantum gravity programs. This book shows moreover that eight of the nine facets of the Problem of Time already occur upon entertaining background independence in classical (rather than quantum) physics. By this development, and interpreting shape theory as modelling background independence, this book further establishes background independence as a field of study. Background independent mechanics, as well as minisuperspace (spatially homogeneous) models of GR and perturbations thereabout are used to illustrate these points. As hitherto formulated, the different facets of the Problem of Time greatly interfere with each others' attempted resolutions. This book explains how, none the less, a local resolution of the Problem of Time can be arrived at after various reconceptualizations of the facets and reformulations of their mathematical implementation. Self-contained appendices on mathematical methods for basic and foundational quantum gravity are included. Finally, this book outlines how supergravity is refreshingly different from GR as a realization of background independence, and what background independence entails at the topological level and beyond. |
| problem book in relativity and gravitation: Problem Book in Relativity and Gravitation , 1973 |
| problem book in relativity and gravitation: Advanced General Relativity John Stewart, John M. Stewart, 1993-11-26 A self-contained introduction to advanced general relativity. |
| problem book in relativity and gravitation: General Relativity and Gravitation B. Bertotti, F. de Felice, Alessandro Pascolini, 1984-09-30 The Tenth International Conference on General Relativity and Gravitation (GR10) was held from July 3 to July 8, 1983, in Padova, Italy. These Conferences take place every three years, under the auspices of the International Society on General Relativity and Gravitation, with the purpose of assessing the current research in the field, critically discussing the prog ress made and disclosing the points of paramount im portance which deserve further investigations. The Conference was attended by about 750 scientists active in the various subfields in which the current research on gravitation and general relativity is ar ticulated, and more than 450 communications were sub mitted. In order to fully exploit this great occur rence of experience and creative capacity, and to pro mote individual contributions to the collective know ledge, the Conference was given a structure of work shops on the most active topics and of general sessions in which the Conference was addressed by invited speakers on general reviews or recent major advance ments of the field. The individual communications were collected in a two-volume publication made available to the participants upon their arrival and widely distributed to Scientific Institutions and Research Centres. |
| problem book in relativity and gravitation: A First Course in General Relativity Bernard F. Schutz, 1985-01-31 This textbook develops general relativity and its associated mathematics from a minimum of prerequisites, leading to a physical understanding of the theory in some depth. |
| problem book in relativity and gravitation: Gravity from the Ground Up Bernard Schutz, 2003-12-04 This book invites the reader to understand our Universe, not just marvel at it. From the clock-like motions of the planets to the catastrophic collapse of a star into a black hole, gravity controls the Universe. Gravity is central to modern physics, helping to answer the deepest questions about the nature of time, the origin of the Universe and the unification of the forces of nature. Linking key experiments and observations through careful physical reasoning, the author builds the reader's insight step-by-step from simple but profound facts about gravity on Earth to the frontiers of research. Topics covered include the nature of stars and galaxies, the mysteries of dark matter and dark energy, black holes, gravitational waves, inflation and the Big Bang. Suitable for general readers and for undergraduate courses, the treatment uses only high-school level mathematics, supplemented by optional computer programs, to explain the laws of physics governing gravity. |
| problem book in relativity and gravitation: Alien Oceans Kevin Hand, 2020-04-07 Inside the epic quest to find life on the water-rich moons at the outer reaches of the solar system Where is the best place to find life beyond Earth? We often look to Mars as the most promising site in our solar system, but recent scientific missions have revealed that some of the most habitable real estate may actually lie farther away. Beneath the frozen crusts of several of the small, ice-covered moons of Jupiter and Saturn lurk vast oceans that may have existed for as long as Earth, and together may contain more than fifty times its total volume of liquid water. Could there be organisms living in their depths? Alien Oceans reveals the science behind the thrilling quest to find out. Kevin Peter Hand is one of today's leading NASA scientists, and his pioneering research has taken him on expeditions around the world. In this captivating account of scientific discovery, he brings together insights from planetary science, biology, and the adventures of scientists like himself to explain how we know that oceans exist within moons of the outer solar system, like Europa, Titan, and Enceladus. He shows how the exploration of Earth's oceans is informing our understanding of the potential habitability of these icy moons, and draws lessons from what we have learned about the origins of life on our own planet to consider how life could arise on these distant worlds. Alien Oceans describes what lies ahead in our search for life in our solar system and beyond, setting the stage for the transformative discoveries that may await us. |
| problem book in relativity and gravitation: Spacetime and Geometry: An Introduction to General Relativity Sean Carroll, 2014-03-20 Spacetime and Geometry: An Introduction to General Relativity provides a lucid and thoroughly modern introduction to general relativity for advanced undergraduates and graduate students. It introduces modern techniques and an accessible and lively writing style to what can often be a formal and intimidating subject. Readers are led from physics of flat spacetime (special relativity), through the intricacies of differential geometry and Einstein's equations, and on to exciting applications such as black holes, gravitational radiation, and cosmology. Subtle points are illuminated throughout the text by careful and entertaining exposition. A straightforward and lucid approach, balancing mathematical rigor and physical insight, are hallmarks of this important text. The full text downloaded to your computer With eBooks you can: search for key concepts, words and phrases make highlights and notes as you study share your notes with friends eBooks are downloaded to your computer and accessible either offline through the Bookshelf (available as a free download), available online and also via the iPad and Android apps. Upon purchase, you'll gain instant access to this eBook. Time limit The eBooks products do not have an expiry date. You will continue to access your digital ebook products whilst you have your Bookshelf installed. |
| problem book in relativity and gravitation: Gravitation and Cosmology Steven Weinberg, 1972 Weinberg's 1972 work, in his description, had two purposes. The first was practical to bring together and assess the wealth of data provided over the previous decade while realizing that newer data would come in even as the book was being printed. He hoped the comprehensive picture would prepare the reader and himself to that new data as it emerged. The second was to produce a textbook about general relativity in which geometric ideas were not given a starring role for (in his words) too great an emphasis on geometry can only obscure the deep connections between gravitation and the rest of physics. |
| problem book in relativity and gravitation: Exact Solutions of Einstein's Field Equations Hans Stephani, Dietrich Kramer, Malcolm MacCallum, Cornelius Hoenselaers, Eduard Herlt, 2009-09-24 A paperback edition of a classic text, this book gives a unique survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources. It introduces the foundations of differential geometry and Riemannian geometry and the methods used to characterize, find or construct solutions. The solutions are then considered, ordered by their symmetry group, their algebraic structure (Petrov type) or other invariant properties such as special subspaces or tensor fields and embedding properties. Includes all the developments in the field since the first edition and contains six completely new chapters, covering topics including generation methods and their application, colliding waves, classification of metrics by invariants and treatments of homothetic motions. This book is an important resource for graduates and researchers in relativity, theoretical physics, astrophysics and mathematics. It can also be used as an introductory text on some mathematical aspects of general relativity. |
| problem book in relativity and gravitation: A General Relativity Workbook Thomas A. Moore, 2012-12-10 A General Relativity Workbook is a textbook intended to support a one-semester undergraduate course on general relativity. Through its unique workbook-based design, it enables students to develop a solid mastery of both the physics and the supporting tensor calculus by guiding them to work through the implications. The mathematics is introduced gradually and in a completely physical context. Each chapter, which is designed to correspond to one class session, involves a short overview of the concepts without obscuring derivations or details, followed by a series of boxes that guide students through the process of working things out. This active-learning approach enables students to develop a more secure mastery of the material than more traditional approaches. More than 350 homework problems support further learning. |
| problem book in relativity and gravitation: Three Hundred Years of Gravitation Stephen Hawking, W. Israel, 1987 A collection of reviews by prominent researchers in cosmology, relativity and particle physics commemorates the 300th anniversary of Newton's Philosophiae Naturalis Principia Mathematica. |
| problem book in relativity and gravitation: The Renaissance of General Relativity in Context Alexander S. Blum, Roberto Lalli, Jürgen Renn, 2020-11-12 This contributed volume explores the renaissance of general relativity after World War II, when it transformed from a marginal theory into a cornerstone of modern physics. Chapters explore key historical processes related to the theory of general relativity, in addition to presenting a thorough treatment of the relevant science behind these episodes. A broad historiographical framework is introduced first, thus providing the broad context in which the given computational approaches and case studies occurred. Written by an international and interdisciplinary group of expert authors, these chapters will bring readers to a more complete understanding of Einstein’s theory. Specific topics include: Social and citation networks The Fock-Infeld dispute Wheeler’s turn to gravitation theory The position of general relativity in theories of fundamental interactions The pursuit of a quantum theory of gravity The emergence of dark matter in relation to cosmological models Institutional frameworks for gravitational wave search in Europe The Renaissance of General Relativity in Context is ideal for historians, philosophers, and sociologists of science. Students and researchers in physics will also be interested in the topics explored. |
| problem book in relativity and gravitation: Mass and Motion in General Relativity Luc Blanchet, Alessandro Spallicci, Bernard Whiting, 2011-01-19 From the infinitesimal scale of particle physics to the cosmic scale of the universe, research is concerned with the nature of mass. While there have been spectacular advances in physics during the past century, mass still remains a mysterious entity at the forefront of current research. Our current perspective on gravitation has arisen over millennia, through the contemplation of falling apples, lift thought experiments and notions of stars spiraling into black holes. In this volume, the world’s leading scientists offer a multifaceted approach to mass by giving a concise and introductory presentation based on insights from their respective fields of research on gravity. The main theme is mass and its motion within general relativity and other theories of gravity, particularly for compact bodies. Within this framework, all articles are tied together coherently, covering post-Newtonian and related methods as well as the self-force approach to the analysis of motion in curved space-time, closing with an overview of the historical development and a snapshot on the actual state of the art. All contributions reflect the fundamental role of mass in physics, from issues related to Newton’s laws, to the effect of self-force and radiation reaction within theories of gravitation, to the role of the Higgs boson in modern physics. High-precision measurements are described in detail, modified theories of gravity reproducing experimental data are investigated as alternatives to dark matter, and the fundamental problem of reconciling any theory of gravity with the physics of quantum fields is addressed. Auxiliary chapters set the framework for theoretical contributions within the broader context of experimental physics. The book is based upon the lectures of the CNRS School on Mass held in Orléans, France, in June 2008. All contributions have beenanonymously refereed and, with the cooperation of the authors, revised by the editors to ensure overall consistency. |
| problem book in relativity and gravitation: General Relativity N.M.J. Woodhouse, 2007-03-06 Based on a course taught for years at Oxford, this book offers a concise exposition of the central ideas of general relativity. The focus is on the chain of reasoning that leads to the relativistic theory from the analysis of distance and time measurements in the presence of gravity, rather than on the underlying mathematical structure. Includes links to recent developments, including theoretical work and observational evidence, to encourage further study. |
| problem book in relativity and gravitation: Einstein Gravity in a Nutshell A. Zee, 2013-05-05 An ideal introduction to Einstein's general theory of relativity This unique textbook provides an accessible introduction to Einstein's general theory of relativity, a subject of breathtaking beauty and supreme importance in physics. With his trademark blend of wit and incisiveness, A. Zee guides readers from the fundamentals of Newtonian mechanics to the most exciting frontiers of research today, including de Sitter and anti-de Sitter spacetimes, Kaluza-Klein theory, and brane worlds. Unlike other books on Einstein gravity, this book emphasizes the action principle and group theory as guides in constructing physical theories. Zee treats various topics in a spiral style that is easy on beginners, and includes anecdotes from the history of physics that will appeal to students and experts alike. He takes a friendly approach to the required mathematics, yet does not shy away from more advanced mathematical topics such as differential forms. The extensive discussion of black holes includes rotating and extremal black holes and Hawking radiation. The ideal textbook for undergraduate and graduate students, Einstein Gravity in a Nutshell also provides an essential resource for professional physicists and is accessible to anyone familiar with classical mechanics and electromagnetism. It features numerous exercises as well as detailed appendices covering a multitude of topics not readily found elsewhere. Provides an accessible introduction to Einstein's general theory of relativity Guides readers from Newtonian mechanics to the frontiers of modern research Emphasizes symmetry and the Einstein-Hilbert action Covers topics not found in standard textbooks on Einstein gravity Includes interesting historical asides Features numerous exercises and detailed appendices Ideal for students, physicists, and scientifically minded lay readers Solutions manual (available only to teachers) |
| problem book in relativity and gravitation: Thinking About Space and Time Claus Beisbart, Tilman Sauer, Christian Wüthrich, 2020-09-25 This volume offers an integrated understanding of how the theory of general relativity gained momentum after Einstein had formulated it in 1915. Chapters focus on the early reception of the theory in physics and philosophy and on the systematic questions that emerged shortly after Einstein's momentous discovery. They are written by physicists, historians of science, and philosophers, and were originally presented at the conference titled Thinking About Space and Time: 100 Years of Applying and Interpreting General Relativity, held at the University of Bern from September 12-14, 2017. By establishing the historical context first, and then moving into more philosophical chapters, this volume will provide readers with a more complete understanding of early applications of general relativity (e.g., to cosmology) and of related philosophical issues. Because the chapters are often cross-disciplinary, they cover a wide variety of topics related to the general theory of relativity. These include: Heuristics used in the discovery of general relativity Mach's Principle The structure of Einstein's theory Cosmology and the Einstein world Stability of cosmological models The metaphysical nature of spacetime The relationship between spacetime and dynamics The Geodesic Principle Symmetries Thinking About Space and Time will be a valuable resource for historians of science and philosophers who seek a deeper knowledge of the (early and later) uses of general relativity, as well as for physicists and mathematicians interested in exploring the wider historical and philosophical context of Einstein's theory. |
| problem book in relativity and gravitation: 3+1 Formalism in General Relativity Éric Gourgoulhon, 2012-02-27 This graduate-level, course-based text is devoted to the 3+1 formalism of general relativity, which also constitutes the theoretical foundations of numerical relativity. The book starts by establishing the mathematical background (differential geometry, hypersurfaces embedded in space-time, foliation of space-time by a family of space-like hypersurfaces), and then turns to the 3+1 decomposition of the Einstein equations, giving rise to the Cauchy problem with constraints, which constitutes the core of 3+1 formalism. The ADM Hamiltonian formulation of general relativity is also introduced at this stage. Finally, the decomposition of the matter and electromagnetic field equations is presented, focusing on the astrophysically relevant cases of a perfect fluid and a perfect conductor (ideal magnetohydrodynamics). The second part of the book introduces more advanced topics: the conformal transformation of the 3-metric on each hypersurface and the corresponding rewriting of the 3+1 Einstein equations, the Isenberg-Wilson-Mathews approximation to general relativity, global quantities associated with asymptotic flatness (ADM mass, linear and angular momentum) and with symmetries (Komar mass and angular momentum). In the last part, the initial data problem is studied, the choice of spacetime coordinates within the 3+1 framework is discussed and various schemes for the time integration of the 3+1 Einstein equations are reviewed. The prerequisites are those of a basic general relativity course with calculations and derivations presented in detail, making this text complete and self-contained. Numerical techniques are not covered in this book. |
| problem book in relativity and gravitation: The Einstein Equations and the Large Scale Behavior of Gravitational Fields Piotr T. Chrusciel, Helmut Friedrich, 2012-12-06 The book presents state-of-the-art results on the analysis of the Einstein equations and the large scale structure of their solutions. It combines in a unique way introductory chapters and surveys of various aspects of the analysis of the Einstein equations in the large. It discusses applications of the Einstein equations in geometrical studies and the physical interpretation of their solutions. Open problems concerning analytical and numerical aspects of the Einstein equations are pointed out. Background material on techniques in PDE theory, differential geometry, and causal theory is provided. |
| problem book in relativity and gravitation: The Theory of Space, Time and Gravitation V. Fock, 2015-08-11 The Theory of Space, Time, and Gravitation, 2nd Revised Edition focuses on Relativity Theory and Einstein's Theory of Gravitation and correction of the misinterpretation of the Einsteinian Gravitation Theory. The book first offers information on the theory of relativity and the theory of relativity in tensor form. Discussions focus on comparison of distances and lengths in moving reference frames; comparison of time differences in moving reference frames; position of a body in space at a given instant in a fixed reference frame; and proof of the linearity of the transformation linking two inertial frames. The text then ponders on general tensor analysis, including permissible transformations for space and time coordinates, parallel transport of a vector, covariant differentiation, and basic properties of the curvature tensor. The publication examines the formulation of relativity theory in arbitrary coordinates and principles of the theory of gravitation. Topics include equations of mathematical physics in arbitrary coordinates; integral form of the conservation laws in arbitrary coordinates; variational principle and the energy tensor; and comparison with the statement of the problem in Newtonian theory. The manuscript is a dependable reference for readers interested in the theory of space, time, and gravitation. |
| problem book in relativity and gravitation: The Genesis of General Relativity Jürgen Renn, 2007-06-17 This four-volume work represents the most comprehensive documentation and study of the creation of general relativity. Einstein’s 1912 Zurich notebook is published for the first time in facsimile and transcript and commented on by today’s major historians of science. Additional sources from Einstein and others, who from the late 19th to the early 20th century contributed to this monumental development, are presented here in translation for the first time. The volumes offer detailed commentaries and analyses of these sources that are based on a close reading of these documents supplemented by interpretations by the leading historians of relativity. |
| problem book in relativity and gravitation: Lectures On Gravitation Ashok Das, 2011-01-06 This book is a compilation of the lectures for a one-semester course on gravitation at the University of Rochester. Starting from a simple description of geometry, the topics are systematically developed to the big bang theory with a simple derivation of the cosmic background temperature. Several informative examples are worked out in detail as well. |
| problem book in relativity and gravitation: Gravitational Theories Beyond General Relativity Iberê Kuntz, 2020-08-14 Despite the success of general relativity in explaining classical gravitational phenomena, several problems at the interface between gravitation and high energy physics still remain open. The purpose of this thesis is to explore quantum gravity and its phenomenological consequences for dark matter, gravitational waves and inflation. A new formalism to classify gravitational theories based on their degrees of freedom is introduced and, in light of this classification, it is argued that dark matter is no different from modified gravity. Gravitational waves are shown to be damped due to quantum degrees of freedom. The consequences for gravitational wave events are also discussed. The non-minimal coupling of the Higgs boson to gravity is studied in connection with Starobinsky inflation and its implications for the vacuum instability problem is analyzed. |
| problem book in relativity and gravitation: Introduction to General Relativity Lewis Ryder, 2020-01-16 A student-friendly style, over 100 illustrations, and numerous exercises are brought together in this textbook for advanced undergraduate and beginning graduate students in physics and mathematics. Lewis Ryder develops the theory of general relativity in detail. Covering the core topics of black holes, gravitational radiation, and cosmology, he provides an overview of general relativity and its modern ramifications. The book contains chapters on gravitational radiation, cosmology, and connections between general relativity and the fundamental physics of the microworld. It explains the geometry of curved spaces and contains key solutions of Einstein's equations - the Schwarzschild and Kerr solutions. Mathematical calculations are worked out in detail, so students can develop an intuitive understanding of the subject, as well as learn how to perform calculations. The book also includes topics concerned with the relation between general relativity and other areas of fundamental physics. Selected solutions for instructors are available under Resources. |
| problem book in relativity and gravitation: Gravitation and Spacetime Hans C. Ohanian, Remo Ruffini, 2013-04-08 The third edition of this classic textbook is a quantitative introduction for advanced undergraduates and graduate students. It gently guides students from Newton's gravitational theory to special relativity, and then to the relativistic theory of gravitation. General relativity is approached from several perspectives: as a theory constructed by analogy with Maxwell's electrodynamics, as a relativistic generalization of Newton's theory, and as a theory of curved spacetime. The authors provide a concise overview of the important concepts and formulas, coupled with the experimental results underpinning the latest research in the field. Numerous exercises in Newtonian gravitational theory and Maxwell's equations help students master essential concepts for advanced work in general relativity, while detailed spacetime diagrams encourage them to think in terms of four-dimensional geometry. Featuring comprehensive reviews of recent experimental and observational data, the text concludes with chapters on cosmology and the physics of the Big Bang and inflation. |
| problem book in relativity and gravitation: General Relativity and Cosmology with Engineering Applications Harish Parthasarathy, 2021 This is a reference book for researchers working in the field of general relativity, quantum mechanics and quantum gravity. A major part of the book deals with the formulation of special relativistic mechanics, special relativistic fluid dynamics and its generalization to general relativity where the gravitational field is described by a metric tensor. Emphasis is laid on the fact that the general theory of relativity is of tensorial character under all dieomorphisms of space-time and hence its field equations, namely the Einstein field equations for gravitation, the Maxwell equations in a curved space-time geometry and the fluid dynamical equations in curved space time are all valid for all observers in the universe. The emphasis throughout is on the fact that matter generates a gravitational field described by a metric that has a non-vanishing curvature tensor and hence such space-times are inherently curved, ie, cannot be transformed into Minkowsian form. There is a final section on quantum mechanics and quantum field theory which introduces supersymmetry and quantum gravity to the reader. The reader after going through this book will be sufficiently well equipped to start research in quantum gravity, i.e, background independent physics which is as yet an unsolved problem owing to renormalization problems. Note: T& F does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka. |
PROBLEM Definition & Meaning - Merriam-Webster
The meaning of PROBLEM is a question raised for inquiry, consideration, or solution. How to use problem in a sentence. Synonym Discussion of Problem.
PROBLEM | English meaning - Cambridge Dictionary
PROBLEM definition: 1. a situation, person, or thing that needs attention and needs to be dealt with or solved: 2. a…. Learn more.
Problem - definition of problem by The Free Dictionary
problem - a question raised for consideration or solution; "our homework consisted of ten problems to solve"
What does Problem mean? - Definitions.net
Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an …
problem, n. meanings, etymology and more | Oxford English …
There are nine meanings listed in OED's entry for the noun problem, three of which are labelled obsolete. See ‘Meaning & use’ for definitions, usage, and quotation evidence.
PROBLEM - Definition & Translations | Collins English Dictionary
Discover everything about the word "PROBLEM" in English: meanings, translations, synonyms, pronunciations, examples, and grammar insights - all in one comprehensive guide.
problem - Wiktionary, the free dictionary
May 17, 2025 · problem (comparative more problem, superlative most problem) (of a person or an animal) Difficult to train or guide; unruly. Causing a problem; problematic; troublesome.
Problem - Definition, Meaning & Synonyms | Vocabulary.com
If you are facing something that will be difficult to handle, you have a problem on your hands. A problem is a roadblock in a situation, something that sets up a conflict and forces you to find a …
Problem Definition & Meaning - YourDictionary
Problem definition: A question to be considered, solved, or answered.
Problem Definition & Meaning | Britannica Dictionary
PROBLEM meaning: 1 : something that is difficult to deal with something that is a source of trouble, worry, etc.; 2 : difficulty in understanding something
PROBLEM Definition & Meaning - Merriam-Webster
The meaning of PROBLEM is a question raised for inquiry, consideration, or solution. How to use problem in a sentence. Synonym Discussion of Problem.
PROBLEM | English meaning - Cambridge Dictionary
PROBLEM definition: 1. a situation, person, or thing that needs attention and needs to be dealt with or solved: 2. a…. Learn more.
Problem - definition of problem by The Free Dictionary
problem - a question raised for consideration or solution; "our homework consisted of ten problems to solve"
What does Problem mean? - Definitions.net
Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to …
problem, n. meanings, etymology and more | Oxford English …
There are nine meanings listed in OED's entry for the noun problem, three of which are labelled obsolete. See ‘Meaning & use’ for definitions, usage, and quotation evidence.
PROBLEM - Definition & Translations | Collins English Dictionary
Discover everything about the word "PROBLEM" in English: meanings, translations, synonyms, pronunciations, examples, and grammar insights - all in one comprehensive guide.
problem - Wiktionary, the free dictionary
May 17, 2025 · problem (comparative more problem, superlative most problem) (of a person or an animal) Difficult to train or guide; unruly. Causing a problem; problematic; troublesome.
Problem - Definition, Meaning & Synonyms | Vocabulary.com
If you are facing something that will be difficult to handle, you have a problem on your hands. A problem is a roadblock in a situation, something that sets up a conflict and forces you to find a …
Problem Definition & Meaning - YourDictionary
Problem definition: A question to be considered, solved, or answered.
Problem Definition & Meaning | Britannica Dictionary
PROBLEM meaning: 1 : something that is difficult to deal with something that is a source of trouble, worry, etc.; 2 : difficulty in understanding something
