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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.
In this short book, renowned theoretical physicist and author Carlo Rovelli gives a straightforward introduction to Einstein's General Relativity, our current theory of gravitation. Focusing on conceptual clarity, he derives all the basic results in the simplest way, taking care to explain the physical, philosophical and mathematical ideas at the heart of “the most beautiful of all scientific theories”. Some of the main applications of General Relativity are also explored, for example, black holes, gravitational waves and cosmology, and the book concludes with a brief introduction to quantum gravity. Written by an author well known for the clarity of his presentation of scientific ideas, this concise book will appeal to university students looking to improve their understanding of the principal concepts, as well as science-literate readers who are curious about the real theory of General Relativity, at a level beyond a popular science treatment.
This second edition of Introduction to Cosmology is an exciting update of an award-winning textbook. It is aimed primarily at advanced undergraduate students in physics and astronomy, but is also useful as a supplementary text at higher levels. It explains modern cosmological concepts, such as dark energy, in the context of the Big Bang theory. Its clear, lucid writing style, with a wealth of useful everyday analogies, makes it exceptionally engaging. Emphasis is placed on the links between theoretical concepts of cosmology and the observable properties of the universe, building deeper physical insights in the reader. The second edition includes recent observational results, fuller descriptions of special and general relativity, expanded discussions of dark energy, and a new chapter on baryonic matter that makes up stars and galaxies. It is an ideal textbook for the era of precision cosmology in the accelerating universe.
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.
The book aims to expound the general theory of relativity with a mathematical point of view. Catering to the needs of postgraduate students and researchers in the field of astrophysics and mathematical physics, it offers the readers a comprehensive understanding of the advanced topics of the subject matter. It specifically discusses the mathematical foundation of tensor calculus, gives a background of geodesics, Einstein's field equations, linearised gravity, spacetime of spherically symmetric distribution of matter and black holes, and particle and photon orbits in spacetime. Apart from the formulation of general relativity, Lie derivatives and its applications, and causality of spacetime are also discussed in detail. Certain preliminary concepts of extrinsic curvature, Lagrangian formalism of general theory of relativity and 3 + 1 decomposition of space-time are covered and are provided in the book as appendices.
Numerical relativity has emerged as the key tool to model gravitational waves - recently detected for the first time - that are emitted when black holes or neutron stars collide. This book provides a pedagogical, accessible, and concise introduction to the subject. Relying heavily on analogies with Newtonian gravity, scalar fields and electromagnetic fields, it introduces key concepts of numerical relativity in a context familiar to readers without prior expertise in general relativity. Readers can explore these concepts by working through numerous exercises, and can see them 'in action' by experimenting with the accompanying Python sample codes, and so develop familiarity with many techniques commonly employed by publicly available numerical relativity codes. This is an attractive, student-friendly resource for short courses on numerical relativity, as well as providing supplementary reading for courses on general relativity and computational physics.
The Cosmic Microwave Background (CMB), the radiation left over from the Big Bang, is arguably the most important topic in modern cosmology. Its theory and observation have revolutionized cosmology from an order-of-magnitude science to a precision science. This graduate textbook describes CMB physics from first principles in a detailed yet pedagogical way, assuming only that the reader has a working knowledge of General Relativity. Among the changes in this second edition are new chapters on non-Gaussianities in the CMB and on large-scale structure, and extended discussions on lensing and baryon acoustic oscillations, topics that have developed significantly in the last decade. Discussions of CMB experiments have been updated from WMAP data to the new Planck data. The CMB success story in estimating cosmological parameters is then treated in detail, conveying the beauty of the interplay of theoretical understanding and precise experimental measurements.
The large-scale structure of the Universe is dominated by vast voids with galaxies clustered in knots, sheets, and filaments, forming a great 'cosmic web'. In this personal account of the major astronomical developments leading to this discovery, we learn from Laird A. Thompson, a key protagonist, how the first 3D maps of galaxies were created. Using non-mathematical language, he introduces the standard model of cosmology before explaining how and why ideas about cosmic voids evolved, referencing the original maps, reproduced here. His account tells of the competing teams of observers, racing to publish their results, the theorists trying to build or update their models to explain them, and the subsequent large-scale survey efforts that continue to the present day. This is a well-documented account of the birth of a major pillar of modern cosmology, and a useful case study of the trials surrounding how this scientific discovery became accepted.
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.
Is the universe fine-tuned for complexity, life, or something else? This comprehensive overview of fine-tuning arguments in physics, with contributions from leading researchers in their fields, sheds light on this often used but seldom understood topic. Each chapter reviews a specific subject in modern physics, such as dark energy, inflation, or solar system formation, and discusses whether any parameters in our current theories appear to be fine-tuned and, if so, to what degree. Connections and differences between these fine-tuning arguments are made clear, and detailed mathematical derivations of various fine-tuned parameters are given. This accessible yet precise introduction to fine-tuning in physics will aid students and researchers across astrophysics, atomic and particle physics and cosmology, as well as all those working at the intersections of physics and philosophy.
The two pillars of modern physics are general relativity and quantum field theory, the former describes the large scale structure and dynamics of space-time, the latter, the microscopic constituents of matter. Combining the two yields quantum field theory in curved space-time, which is needed to understand quantum field processes in the early universe and black holes, such as the well-known Hawking effect. This book examines the effects of quantum field processes back-reacting on the background space-time which become important near the Planck time (10-43 sec). It explores the self-consistent description of both space-time and matter via the semiclassical Einstein equation of semiclassical gravity theory, exemplified by the inflationary cosmology, and fluctuations of quantum fields which underpin stochastic gravity, necessary for the description of metric fluctuations (space-time foams). Covering over four decades of thematic development, this book is a valuable resource for researchers interested in quantum field theory, gravitation and cosmology.
Free yourself from cosmological tyranny! Everything started in a Big Bang? Invisible dark matter? Black holes? Why accept such a weird cosmos? For all those who wonder about this bizarre universe, and those who want to overthrow the Big Bang, this handbook gives you 'just the facts': the observations that have shaped these ideas and theories. While the Big Bang holds the attention of scientists, it isn't perfect. The authors pull back the curtains, and show how cosmology really works. With this, you will know your enemy, cosmic revolutionary - arm yourself for the scientific arena where ideas must fight for survival! This uniquely-framed tour of modern cosmology gives a deeper understanding of the inner workings of this fascinating field. The portrait painted is realistic and raw, not idealized and airbrushed - it is science in all its messy detail, which doesn't pretend to have all the answers.
Spacetime and Geometry is an introductory textbook on general relativity, specifically aimed at students. Using a lucid style, Carroll first covers the foundations of the theory and mathematical formalism, providing an approachable introduction to what can often be an intimidating subject. Three major applications of general relativity are then discussed: black holes, perturbation theory and gravitational waves, and cosmology. Students will learn the origin of how spacetime curves (the Einstein equation) and how matter moves through it (the geodesic equation). They will learn what black holes really are, how gravitational waves are generated and detected, and the modern view of the expansion of the universe. A brief introduction to quantum field theory in curved spacetime is also included. A student familiar with this book will be ready to tackle research-level problems in gravitational physics.
Interpreting general relativity relies on a proper description of non-inertial frames and Dirac observables. This book describes global non-inertial frames in special and general relativity. The first part covers special relativity and Minkowski space time, before covering general relativity, globally hyperbolic Einstein space-time, and the application of the 3+1 splitting method to general relativity. The author uses a Hamiltonian description and the Dirac–Bergmann theory of constraints to show that the transition between one non-inertial frame and another is a gauge transformation, extra variables describing the frame are gauge variables, and the measureable matter quantities are gauge invariant Dirac observables. Point particles, fluids and fields are also discussed, including how to treat the problems of relative times in the description of relativistic bound states, and the problem of relativistic centre of mass. Providing a detailed description of mathematical methods, the book is perfect for theoretical physicists, researchers and students working in special and general relativity.
This modern introduction to particle physics equips students with the skills needed to develop a deep and intuitive understanding of the physical theory underpinning contemporary experimental results. The fundamental tools of particle physics are introduced and accompanied by historical profiles charting the development of the field. Theory and experiment are closely linked, with descriptions of experimental techniques used at CERN accompanied by detail on the physics of the Large Hadron Collider and the strong and weak forces that dominate proton collisions. Recent experimental results are featured, including the discovery of the Higgs boson. Equations are supported by physical interpretations, and end-of-chapter problems are based on datasets from a range of particle physics experiments including dark matter, neutrino, and collider experiments. A solutions manual for instructors is available online. Additional features include worked examples throughout, a detailed glossary of key terms, appendices covering essential background material, and extensive references and further reading to aid self-study, making this an invaluable resource for advanced undergraduates in physics.
This compact guide presents the key features of general relativity, to support and supplement the presentation in mainstream, more comprehensive undergraduate textbooks, or as a re-cap of essentials for graduate students pursuing more advanced studies. It helps students plot a careful path to understanding the core ideas and basics of differential geometry, as applied to general relativity, without overwhelming them. While the guide doesn't shy away from necessary technicalities, it emphasises the essential simplicity of the main physical arguments. Presuming a familiarity with special relativity (with a brief account in an appendix), it describes how general covariance and the equivalence principle motivate Einstein's theory of gravitation. It then introduces differential geometry and the covariant derivative as the mathematical technology which allows us to understand Einstein's equations of general relativity. The book is supported by numerous worked exampled and problems, and important applications of general relativity are described in an appendix.
Einstein's general theory of relativity is widely considered to be one of the most elegant and successful scientific theories ever developed, and it is increasingly being taught in a simplified form at advanced undergraduate level within both physics and mathematics departments. Due to the increasing interest in gravitational physics, in both the academic and the public sphere, driven largely by widely-publicised developments such as the recent observations of gravitational waves, general relativity is also one of the most popular scientific topics pursued through self-study. Modern General Relativity introduces the reader to the general theory of relativity using an example-based approach, before describing some of its most important applications in cosmology and astrophysics, such as gamma-ray bursts, neutron stars, black holes, and gravitational waves. With hundreds of worked examples, explanatory boxes, and end-of-chapter problems, this textbook provides a solid foundation for understanding one of the towering achievements of twentieth-century physics.
Recent cosmological observations have posed a challenge for traditional theories of gravity: what is the force driving the accelerated expansion of the universe? What if dark energy or dark matter do not exist and what we observe is a modification of the gravitational interaction that dominates the universe at large scales? Various extensions to Einstein's General Theory of Relativity have been proposed, and this book presents a detailed theoretical and phenomenological analysis of several leading, modified theories of gravity. Theories with generalised curvature-matter couplings are first explored, followed by hybrid metric-Palatini gravity. This timely book first discusses key motivations behind the development of these modified gravitational theories, before presenting a detailed overview of their subsequent development, mathematical structure, and cosmological and astrophysical implications. Covering recent developments and with an emphasis on astrophysical and cosmological applications, this is the perfect text for graduate students and researchers.
The 2015 centenary of the publication of Einstein's general theory of relativity, and the first detection of gravitational waves have focused renewed attention on the question of whether Einstein was right. This review of experimental gravity provides a detailed survey of the intensive testing of Einstein's theory of gravity, including tests in the emerging strong-field dynamical regime. It discusses the theoretical frameworks needed to analyze gravitational theories and interpret experiments. Completely revised and updated, this new edition features coverage of new alternative theories of gravity, a unified treatment of gravitational radiation, and the implications of the latest binary pulsar observations. It spans the earliest tests involving the Solar System to the latest tests using gravitational waves detected from merging black holes and neutron stars. It is a comprehensive reference for researchers and graduate students working in general relativity, cosmology, particle physics and astrophysics.
Magnetic fields pervade the universe and play an important role in many astrophysical processes. However, they require specialised observational tools, and are challenging to model and understand. This volume provides a unified view of magnetic fields across astrophysical and cosmological contexts, drawing together disparate topics that are rarely covered together. Written by the lecturers of the XXV Canary Islands Winter School, it offers a self-contained introduction to cosmic magnetic fields on a range of scales. The connections between the behaviours of magnetic fields in these varying contexts are particularly emphasised, from the relatively small and close ranges of the Sun, planets and stars, to galaxies and clusters of galaxies, as well as on cosmological scales. Aimed at young researchers and graduate students, this up-to-date review uniquely brings together a subject often tackled by disconnected communities, conveying the latest advances as well as highlighting the limits of our current understanding.