This book provides an accessible, yet thorough, introduction to special and general relativity, crafted and class-tested over many years of teaching. Suitable for advanced undergraduate and graduate students, this book provides clear descriptions of how to approach the mathematics and physics involved. It is also contains the latest exciting developments in the field, including dark energy, gravitational waves, and frame dragging. The table of contents has been carefully developed in consultation with a large number of instructors teaching courses worldwide, to ensure its wide applicability to modules on relativity and gravitation. Features: A clear, accessible writing style, presenting a sophisticated approach to the subject, that remains suitable for advanced undergraduate students and above Class-tested over many years To be accompanied by a partner volume on 'Advanced Topics' for students to further extend their learning

Teaching Einstein s general relativity at introductory level poses problems because students cannot begin to appreciate the basics of the theory unless they learn a sufficient amount of Riemannian geometry. Most elementary books take the easy course of telling the students a few working rules stripping the mathematical details to a minimum while the advanced books take the mathematical background for granted. Students eager to study Einstein s theory at a deeper level are forced to learn the mathematical background on their own and they feel lost because pure mathematical texts on geometry are too abstract and formal.

The present book solves this pedagogical problem in a unique way by dividing the book into three parts. Essential concepts of Riemannian geometry are introduced in Part I (four chapters) through Gauss work on curvature of surfaces using only ordinary calculus. A first acquaintance with Einstein s theory can then be made. Only after this first brush with both physics and mathematics of relativity, a proper, detailed mathematical background is developed in the next six chapters in Part II. The third part then recaptures all the basic concepts of general relativity and leaves the student with a sound preparation for learning advanced topics.

My aim has been that after learning from this book a student should not feel discouraged when she opens advanced texts on general relativity for further reading."

This book presents the first English translation of the original French treatise "La Physique d'Einstein" written by the young Georges Lemai tre in 1922, only six years after the publication of Albert Einstein's theory of General Relativity. It includes an historical introduction and a critical edition of the original treatise in French supplemented by the author's own later additions and corrections. Monsignor Georges Lemai tre can be considered the founder of the "Big Bang Theory" and a visionary architect of modern Cosmology. The scientific community is only beginning to grasp the full extent of the legacy of this towering figure of 20th century physics. Against the best advice of the greatest names of his time, the young Lemai tre was convinced, solely through the study of Einstein's theory of General Relativity, that space and time must have had a beginning with a tremendous "Big Bang" from a "quantum primeval atom" resulting in an ever-expanding Universe with a positive cosmological constant. But how did the young Lemai tre, essentially on his own, come to grips with the physics of Einstein? A year before his ordination as a diocesan priest, he submitted the audacious treatise, published in this book, that was to earn him Fellowships to study at Cambridge, MIT and Harvard, and launched him on a scientific path of ground-breaking discoveries. Almost a century after Lemai tre's seminal publications of 1927 and 1931, this highly pedagogical treatise is still of timely interest to young minds and remains of great value from a history of science perspective.

This textbook is suitable for a one-semester introduction to General Relativity for advanced undergraduates in physics and engineering. The book is concise so that the entire material can be covered in the one-semester time frame. Many of the calculations are done in detail, without difficult mathematics, to help the students. Though concise, the theory development is lucid and the readers are exposed to possible analytic calculations.In the second edition, the famous twin paradox with acceleration is solved in full from the accelerated observer's frame. The findings of the Event Horizon Telescope (EHT) collaboration, who captured the first ever image of a black hole, are discussed in detail. The geodetic and frame drag precessions of gyroscopes in orbit about a rotating Earth are worked out and the Gravity Probe B (GPB) experiment is discussed. Also in the second edition are some new exercise problems.Resources are provided to instructors who adopt this textbook for their courses. Adopting instructors can print and copy portions of these resources solely for their teaching needs. All instructional resources are furnished for informational use only, and are subject to change without notice.

This textbook is suitable for a one-semester introduction to General Relativity for advanced undergraduates in physics and engineering. The book is concise so that the entire material can be covered in the one-semester time frame. Many of the calculations are done in detail, without difficult mathematics, to help the students. Though concise, the theory development is lucid and the readers are exposed to possible analytic calculations.In the second edition, the famous twin paradox with acceleration is solved in full from the accelerated observer's frame. The findings of the Event Horizon Telescope (EHT) collaboration, who captured the first ever image of a black hole, are discussed in detail. The geodetic and frame drag precessions of gyroscopes in orbit about a rotating Earth are worked out and the Gravity Probe B (GPB) experiment is discussed. Also in the second edition are some new exercise problems.Resources are provided to instructors who adopt this textbook for their courses. Adopting instructors can print and copy portions of these resources solely for their teaching needs. All instructional resources are furnished for informational use only, and are subject to change without notice.

1 IN THE MONOGRAPH SERIES directed by Henri Villat , several fasci- cules have been devoted to Relativity. First there are the general presentations ofTh. De Donder (nos. 8, 14, 43, 58), and then those more specifically devoted to Einsteinian gravitation - notably Georges Darmois's contribution (no. 25) and that of J. Haag (no. 46) on the Schwarzschild problem. The present fascicule takes its place alongside the two latter monographs, but it has been conceived and composed in such a way that it may be read and understood by anyone with a knowledge of the principles of Absolute Differential Calculus and of Relativity - either from the original exposi- tions of Einstein, Weyl, or Eddington, or, in French, from Cartan's excel- 2 lent works (for everything having to do with mathematical theories) and 3 from Chazy's (for Relativity and Celestial Mechanics), or naturally from Levi-Civita's The Absolute Differential Calculus (first edition, London and Glasgow, Blackie and Son, 1927) where the two original papers written in Italian are brought together: namely, Calcolo differenziale assoluto and Fondamenti di meccanica relativistica (Bologna, Zanichelli). As for the present fascicule, it is hardly necessary to point out that, as its title indicates, we seek to establish in the simplest possible terms the rela- tivistic aspect of what Newton and those who followed him regarded as the key to ordinary Celestial Mechanics.

The fourth edition contains seven new sections with chapters on General Relativity, Gravitational Waves and Relativistic Cosmology. The text has been thoroughly revised and additional problems inserted.

The Complete course of Theoretical Physics by Landau and Lifshitz, recognized as two of the world's outstanding physicists, is published in full by Butterworth-Heinemann. It comprises nine volumes, covering all branches of the subject; translations from the Russian are by leading scientists.

Observing our Universe and its evolution with ever increasing sensitivity from ground-based or space-borne telescopes is posing great challenges to Fundamental Physics and Astronomy. The remnant cosmic microwave background, as beautifully measured by successive space missions COBE, WMAP, and now PLANCK, provides a unique probe of the very early stages of our Universe. The red-shift of atomic lines in distant galaxies, the dynamics of pulsars, the large scale structure of galaxies, and black holes are a few manifestations of the theory of General Relativity. Yet, today, we understand only 4% of the mass of our Universe, the rest being called dark energy and dark matter, both of unknown origin! A second family of space missions is currently emerging; rather than designing ever more re nedobservationalinstruments,physicistsandengineersseekalsotousethespaceenvironment to perform high-precision tests of the fundamental laws of physics. The technology required for such tests has become available only over the course of the last decades. Clocks of high accuracy are an example. They are based on advances in atomic and laser physics, such as cold atoms, enabling a new generation of highly sensitive quantum sensors for ground and space experiments. Two experiments in space have now tested Einstein's relativity theory: * Several decades ago, Gravity Probe A con rmed the accuracy of the gravitational red-shift ?5 according to general relativity to a level of 7x 10 [R. F. C. Vessot et al. , Test of Relativistic Gravitation with a Space-Borne Hydrogen Maser, Phys. Rev. Lett. 45, 2081-2084 (1980)].

After Physics presents ambitious new essays about some of the deepest questions at the foundations of physics, by the physicist and philosopher David Albert. The book's title alludes to the close connections between physics and metaphysics, much in evidence throughout these essays. It also alludes to the work of imagining what it would be like for the project of physical science-considered as an investigation into the fundamental laws of nature-to be complete. Albert argues that the difference between the past and the future-traditionally regarded as a matter for metaphysical or conceptual or linguistic or phenomenological analysis-can be understood as a mechanical phenomenon of nature. In another essay he contends that all versions of quantum mechanics that are compatible with the special theory of relativity make it impossible, even in principle, to present the entirety of what can be said about the world as a narrative sequence of "befores" and "afters." Any sensible and realistic way of solving the quantum-mechanical measurement problem, Albert claims in yet another essay, is ultimately going to force us to think of particles and fields, and even the very space of the standard scientific conception of the world, as approximate and emergent. Novel discussions of the problem of deriving principled limits on what can be known, measured, or communicated from our fundamental physical theories, along with a sweeping critique of the main attempts at making sense of probabilities in many-worlds interpretations of quantum mechanics, round out the collection.

Compact objects are an important class of astronomical objects in current research. Supermassive black holes play an important role in the understanding of the formation of galaxies in the early Universe. Old white dwarfs are nowadays used to calibrate the age of the Universe. Mergers of neutron stars and black holes are the sources of intense gravitational waves which will be measured in the next ten years by gravitational wave detectors.

Camenzind's Compact Objects in Astrophysics gives a comprehensive introduction and up-to-date overview about the physical processes behind these objects, covering the field from the beginning to most recent results, including all relevant observations.

After a presentation of the taxonomy of compact objects, the basic principles of general relativity are given. The author then discusses in detail the physics and observations of white dwarfs and neutron stars (including the most recent equations of state for neutron star matter), the gravitational field of rapidly rotating compact objects, rotating black holes (including ray tracing and black hole magnetospheres), gravitational waves, and the new understanding of accretion processes by means of the magnetorotational instability of accretion disks.
This modern treatise of compact object astrophysics uses the 3+1 split approach to Einstein's equations, and to relativistic hydrodynamics and magnetohydrodynamics. In each chapter problems and solutions help deepen the understanding of the subject. Both advanced students and researchers will appreciate this book as an advanced textbook and reference on this fascinating field of astrophysics.

The purpose of this book is to give a systematic pedagogical exposition of the quantitative analysis of Wilson lines and gauge-invariant correlation functions in quantum chromodynamics. Using techniques from the previous volume (Wilson Lines in Quantum Field Theory, 2014), an ab initio methodology is developed and practical tools for its implementation are presented. Emphasis is put on the implications of gauge invariance and path-dependence properties of transverse-momentum dependent parton density functions. The latter are associated with the QCD factorization approach to semi-inclusive hadronic processes, studied at currently operating and planned experimental facilities. Contents: Introduction Particle Number Operators in Quantum Mechanics and in Quantum Field Theory Geometry of Quantum Field Theories Basics of Wilson Lines in QCD Gauge-Invariant Parton Densities Simplifying Wilson Line Calculations Brief Literature Guide Conventions and Reference Formulae Integrations Bibliography Index

'Outstanding Academic Title for 2014' by CHOICEEinstein Relatively Simple brings together for the first time an exceptionally clear explanation of both special and general relativity. It is for people who always wanted to understand Einstein's ideas but never thought they could.Told with humor, enthusiasm, and rare clarity, this entertaining book reveals how a former high school drop-out revolutionized our understanding of space and time. From E=mc2 and everyday time travel to black holes and the big bang, Einstein Relatively Simple takes us all, regardless of our scientific backgrounds, on a mind-boggling journey through the depths of Einstein's universe. Along the way, we track Einstein through the perils and triumphs of his life - follow his thinking, his logic, and his insights - and chronicle the audacity, imagination, and sheer genius of the man recognized as the greatest scientist of the modern era.In Part I on special relativity we learn how time slows and space shrinks with motion, and how mass and energy are equivalent. Part II on general relativity reveals a cosmos where black holes trap light and stop time, where wormholes form gravitational time machines, where space itself is continually expanding, and where some 13.7 billion years ago our universe was born in the ultimate cosmic event - the Big Bang.

This thoroughly revised 5th edition of Zeh's classic text investigates irreversible phenomena and their foundation in classical, quantum and cosmological settings. It includes new sections on the meaning of probabilities in a cosmological context, irreversible aspects of quantum computers, and various consequences of the expansion of the Universe. In particular, the book offers an analysis of the physical concept of time.

This book shows how one can combine Yang-Mills gauge symmetry and effective Einstein-Grossmann metric tensors to tackle physical problems at microscopic, macroscopic and super-macroscopic length scales. In particular, the combination of gauge symmetry and an effective metric tensor provides a framework for and leads to an alternative dynamics of cosmic expansion based on quantum Yang-Mills gravity at the super-macroscopic limit. Together with the cosmological principle, one can investigate and derive expanding scale factors, the age of the universe, the cosmic redshift, and the Hubble recession velocity. Furthermore, this framework leads to a possible explanation for the late-time accelerated cosmic expansion due to baryon masses and charges. All these discussions are based on the operationally defined space and time coordinates of inertial frames. Finally, this book expounds on the intimate relationship between space-time translation gauge symmetry and the beautiful ideas of the Lie derivative and Pauli's variation. One interesting application of the Lie derivative is to formulate a gravitational theory with an external space-time gauge group, which leads to Yang-Mills gravity.

The Mathematical Principles of Scale Relativity Physics: The Concept of Interpretation explores and builds upon the principles of Laurent Nottale's scale relativity. The authors address a variety of problems encountered by researchers studying the dynamics of physical systems. It explores Madelung fluid from a wave mechanics point of view, showing that confinement and asymptotic freedom are the fundamental laws of modern natural philosophy. It then probes Nottale's scale transition description, offering a sound mathematical principle based on continuous group theory. The book provides a comprehensive overview of the matter to the reader via a generalization of relativity, a theory of colors, and classical electrodynamics. Key Features: Develops the concept of scale relativity interpreted according to its initial definition enticed by the birth of wave and quantum mechanics Provides the fundamental equations necessary for interpretation of matter, describing the ensembles of free particles according to the concepts of confinement and asymptotic freedom Establishes a natural connection between the Newtonian forces and the Planck's law from the point of view of space and time scale transition: both are expressions of invariance to scale transition The work will be of great interest to graduate students, doctoral candidates, and academic researchers working in mathematics and physics.

The historic detection of gravitational waves on September 14, 2015, prompted by the highly energetic fusion of two black holes, has made events in the universe "audible" for the first time. This expansion of the scientific sensorium has opened a new chapter in astronomy and already led to, among others, fascinating new insights about the abundance of black holes, the collision of neutron stars, and the origin of heavy chemical elements. The history of this event, which is epochal for physics, is reconstructed in this book, along with a walk-through of the main principles of how the detectors operate and a discussion of how the search for gravitational waves is conducted. The book concludes with an update of the latest detections and developments to date and a brief look into the future of this exciting research field. This book is accessible to non-specialist readers from a general audience and is also an excellent introduction to the topic for undergraduates in physics. Features: Provides an introduction to the historic discovery of gravitational waves Explains the inner workings of the detectors and the search to find the waves hidden in the data Authored by a renowned specialist involved in the ground-breaking discovery Hartmut Grote is a Professor of physics at Cardiff University, UK. His main expertise is in experimental gravitational-wave physics, and he has worked on building and improving gravitational wave detectors for over 20 years. From 2009 to 2017, he was the scientific leader of the British-German gravitational-wave detector: GEO600.

The nature of space and time is one of the most fascinating and fundamental philosophical issues which presently engages at the deepest level with physics. During the last thirty years this notion has been object of an intense critical review in the light of new scientific theories which try to combine the principles of both general relativity and quantum theory-called theories of quantum gravity. This book considers the way string theory shapes its own account of spacetime disappearance from the fundamental level.

The hydrogen Lyman-alpha line is of utmost importance to many fields of astrophysics. This UV line being conveniently redshifted with distance to the visible and even near infrared wavelength ranges, it is observable from the ground, and provides the main observational window on the formation and evolution of high redshift galaxies. Absorbing systems that would otherwise go unnoticed are revealed through the Lyman-alpha forest, Lyman-limit, and damped Lyman-alpha systems, tracing the distribution of baryonic matter on large scales, and its chemical enrichment. We are living an exciting epoch with the advent of new instruments and facilities, on board of satellites and on the ground. Wide field and very sensitive integral field spectrographs are becoming available on the ground, such as MUSE at the ESO VLT. The giant E-ELT and TMT telescopes will foster a quantum leap in sensitivity and both spatial and spectroscopic resolution, to the point of being able, perhaps, to measure directly the acceleration of the Hubble flow. In space, the JWST will open new possibilities to study the Lyman-alpha emission of primordial galaxies in the near infrared. As long as the Hubble Space Telescope will remain available, the UV-restframe properties of nearby galaxies will be accessible to our knowledge. Therefore, this Saas-Fee course appears very timely and should meet the interest of many young researchers.

With a focus on modified gravity this book presents a review of the recent developments in the fields of gravity and cosmology, presenting the state of the art, high-lighting the open problems, and outlining the directions of future research. General Relativity and the CDM framework are currently the standard lore and constitute the concordance paradigm of cosmology. Nevertheless, long-standing open theoretical issues, as well as possible new observational ones arising from the explosive development of cosmology in the last two decades, offer the motivation and lead a large amount of research to be devoted in constructing various extensions and modifications. In this review all extended theories and scenarios are first examined under the light of theoretical consistency, and are then applied in various geometrical backgrounds, such as the cosmological and the spherical symmetric ones. Their predictions at both the background and perturbation levels, and concerning cosmology at early, intermediate and late times, are then confronted with the huge amount of observational data that astrophysics and cosmology has been able to offer in the last two decades. Theories, scenarios and models that successfully and efficiently pass the above steps are classified as viable and are candidates for the description of Nature, allowing readers to get a clear overview of the state of the art and where the field of modified gravity is likely to go. This work was performed in the framework of the COST European Action "Cosmology and Astrophysics Network for Theoretical Advances and Training Actions" - CANTATA.

Written by a former Olympiad student, Wang Jinhui, and a Physics Olympiad national trainer, Bernard Ricardo, Competitive Physics delves into the art of solving challenging physics puzzles. This book not only expounds a multitude of physics topics from the basics but also illustrates how these theories can be applied to problems, often in an elegant fashion. With worked examples that depict various problem-solving sleights of hand and interesting exercises to enhance the mastery of such techniques, readers will hopefully be able to develop their own insights and be better prepared for physics competitions. Ultimately, problem-solving is a craft that requires much intuition. Yet this intuition, perhaps, can only be honed by trudging through an arduous but fulfilling journey of enigmas.This is the second part of a two-volume series and will mainly analyze thermodynamics, electromagnetism and special relativity. A brief overview of geometrical optics is also included.

This is the second and final volume of Dutch physicist Hendrik Antoon Lorentz's scientific correspondence with Dutch colleagues, including Pieter Zeeman and Paul Ehrenfest. These 294 letters cover multiple subjects, ranging from pure mathematics to magneto-optics and wave mechanics. They reveal much about their author, including Lorentz's surprisingly active involvement in experimental matters in the first decades of his career. Letters are also devoted to general relativity, Lorentz's 1908 lecture on radiation theory, and his receipt of the Nobel Prize along with Zeeman in 1902. The letters are presented in their original language; Dutch originals are accompanied by English translations. A concise biography of Lorentz is also included.

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

This book is intended to engage the students in the elegance of electrodynamics and special relativity, whilst giving them the tools to begin graduate study. Here, from the basis of experiment, the authors first derive the Maxwell equations and special relativity. Introducing the mathematical framework of generalized tensors, the laws of mechanics, Lorentz force and the Maxwell equations are then cast in manifestly covariant form. This provides the basis for graduate study in field theory, high energy astrophysics, general relativity and quantum electrodynamics. As the title suggests, this book is "electrodynamics lite". The journey through electrodynamics is kept as brief as possible, with minimal diversion into details, so that the elegance of the theory can be appreciated in a holistic way. It is written in an informal style and has few prerequisites; the derivation of the Maxwell equations and their consequences is dealt with in the first chapter. Chapter 2 is devoted to conservation equations in tensor formulation; here, Cartesian tensors are introduced. Special relativity and its consequences for electrodynamics are introduced in Chapter 3 and cast in four-vector form, and here, the authors introduce generalized tensors. Finally, in Chapter 4, Lorentz frame invariant electrodynamics is developed. Supplementary material and examples are provided by the two sets of problems. The first is revision of undergraduate electromagnetism, to expand on the material in the first chapter. The second is more advanced corresponding to the remaining chapters, and its purpose is twofold: to expand on points that are important, but not essential, to derivation of manifestly covariant electrodynamics, and to provide examples of manipulation of cartesian and generalized tensors. As these problems introduce material not covered in the text, they are accompanied by full worked solutions. The philosophy here is to facilitate learning by problem solving, as well as by studying the text. Extensive appendices for vector relations, unit conversion and so forth are given with graduate study in mind.