This book brings Einstein's general relativity into action in new ways at scales ranging from the tiny Planck scale to the scale of immense galactic clusters. It presents the case that Einstein's theory of gravity can describe the observed dynamics of galaxies without invoking the unknown "dark matter" required in models based on Newtonian gravity.

Drawing on the author's experience as a lecturer and on his own research, the book covers the essentials of Einstein's special and general relativity at a level accessible to undergraduate students. The early chapters provide a compact introduction to relativity for readers who have little or no background in the subject. Hermann Bondi's very transparent approach to special relativity is expanded to resolve the "twin paradox" using only elementary mathematics. In later chapters, general relativity is used to extend the concept of the Planck scale, to address the role of the cosmological term and to analyze the concept of "time machines."

This book presents a collection of focused review papers on the advances in topics in modern astronomy, astrophysics, cosmology and planetary science. The chapters are written by expert members of an EU-funded ERASMUS+ program of strategic partnership between several European institutes. The 13 reviews comprise the topics: Space debris, optical measurements Meteors, light from comets and asteroids Extrasolar enigmas: from disintegrating exoplanets to exo-asteroids Physical conditions and chemical abundances in photoionized nebulae from optical spectra Observational Constraints on the Common Envelope Phase A modern guide to quantitative spectroscopy of massive OB stars Explosion mechanisms of core-collapse supernovae and their observational signatures Low-mass and substellar eclipsing binaries in stellar clusters Globular cluster systems and Galaxy Formation Hot atmospheres of galaxies, groups, and clusters of galaxies The establishment of the Standard Cosmological Model through observations Exploiting solar visible-range observations by inversion techniques: from flows in the solar subsurface to a flaring atmosphere Starburst galaxies The book is intended for the general astronomical community as well as for advanced students who could use it as a guideline, inspiration and overview for their future careers in astronomy.

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

This book, first appearing in German in 2004 under the title Spezielle Relativitatstheorie fur Studienanfanger, offers access to the special theory of relativity for readers with a background in mathematics and physics comparable to a high school honors degree. All mathematical and physical competence required beyond that level is gradually developed through the book, as more advanced topics are introduced. The full tensor formalism, however, is dispensed with as it would only be a burden for the problems to be dealt with. Eventually, a substantial and comprehensive treatise on special relativity emerges which, with its gray-shaded formulary, is an invaluable reference manual for students and scientists alike.Some crucial results are derived more than once with different approaches: the Lorentz transformation in one spatial direction three times, the Doppler formula four times, the Lorentz transformation in two directions twice; also twice the unification of electric and magnetic forces, the velocity addition formula, as well as the aberration formula. Beginners will be grateful to find several routes to the goal; moreover, for a theory like relativity, it is of fundamental importance to demonstrate that it is self-contained and without contradictions.Author's website: www.relativity.ch.

Differentilil Geometry and Relativity Theory: An Introduction approaches relativity asa geometric theory of space and time in which gravity is a manifestation of space-timecurvature, rathe1 than a force. Uniting differential geometry and both special and generalrelativity in a single source, this easy-to-understand text opens the general theory of relativityto mathematics majors having a backgr.ound only in multivariable calculus and linearalgebra.The book offers a broad overview of the physical foundations and mathematical details ofrelativity, and presents concrete physical interpretations of numerous abstract concepts inRiemannian geometry. The work is profusely illustrated with diagrams aiding in the understandingof proofs and explanations. Appendices feature important material on vectoranalysis and hyperbolic functions.Differential Geometry and Relativity Theory: An Introduction serves as the ideal textfor high-level undergraduate couues in mathematics and physics, and includes a solutionsmanual augmenting classroom study. It is an invaluable reference for mathematicians interestedin differential and IUemannian geometry, or the special and general theories ofrelativity

A working knowledge of Einstein's theory of general relativity is an essential tool for every physicist today. This self-contained book is an introductory text on the subject aimed at first-year graduate students, or advanced undergraduates, in physics that assumes only a basic understanding of classical Lagrangian mechanics. The mechanics problem of a point mass constrained to move without friction on a two-dimensional surface of arbitrary shape serves as a paradigm for the development of the mathematics and physics of general relativity. After reviewing special relativity, the basic principles of general relativity are presented, and the most important applications are discussed. The final special topics section guides the reader through a few important areas of current research. This book will allow the reader to approach the more advanced texts and monographs, as well as the continual influx of fascinating new experimental results, with a deeper understanding and sense of appreciation.

A working knowledge of Einstein's theory of general relativity is an essential tool for every physicist today. This self-contained book is an introductory text on the subject aimed at first-year graduate students, or advanced undergraduates, in physics that assumes only a basic understanding of classical Lagrangian mechanics. The mechanics problem of a point mass constrained to move without friction on a two-dimensional surface of arbitrary shape serves as a paradigm for the development of the mathematics and physics of general relativity. After reviewing special relativity, the basic principles of general relativity are presented, and the most important applications are discussed. The final special topics section guides the reader through a few important areas of current research. This book will allow the reader to approach the more advanced texts and monographs, as well as the continual influx of fascinating new experimental results, with a deeper understanding and sense of appreciation.

A Broader View of Relativity shows that there is still new life in old physics. The book examines the historical context and theoretical underpinnings of Einstein's theory of special relativity and describes Broad Relativity, a generalized theory of coordinate transformations between inertial reference frames that includes Einstein's special relativity as a special case. It shows how the principle of relativity is compatible with multiple concepts of physical time and how these different procedures for clock synchronization can be useful for thinking about different physical problems, including many-body systems and the development of a Lorentz-invariant thermodynamics. Broad relativity also provides new answers to old questions such as the necessity of postulating the constancy of the speed of light and the viability of Reichenbach's general concept of time. The book also draws on the idea of limiting-four-dimensional symmetry to describe coordinate transformations and the physics of particles and fields in non-inertial frames, particularly those with constant linear accelerations. This new edition expands the discussion on the role that human conventions and unit systems have played in the historical development of relativity theories and includes new results on the implications of broad relativity for clarifying the status of constants that are truly fundamental and inherent properties of our universe.

This book is a comprehensive survey of the current state of knowledge about the dynamics and gravitational properties of cosmic strings treated in the idealized classical approximation as line singularities described by the Nambu-Goto action. The author's purpose is to provide a standard reference to all work that has been published since the mid-1970s and to link this work together in a single conceptual framework and a single notational formalism. A working knowledge of basic general relativity is assumed. The book will be essential reading for researchers and postgraduate students in mathematics, theoretical physics, and astronomy interested in cosmic strings.

This volume of the Encyclopaedia contains three contributions in the field of complex analysis. The topics treated are mean periodicity and convolutionequations, Yang-Mills fields and the Radon-Penrose transform, and stringtheory. The latter two have strong links with quantum field theory and the theory of general relativity. In fact, the mathematical results described inthe book arose from the need of physicists to find a sound mathematical basis for their theories. The authors present their material in the formof surveys which provide up-to-date accounts of current research. The book will be immensely useful to graduate students and researchers in complex analysis, differential geometry, quantum field theory, string theoryand general relativity.

This is the only book on the subject of group theory and Einstein's theory of gravitation. It contains an extensive discussion on general relativity from the viewpoint of group theory and gauge fields. It also puts together in one volume many scattered, original works, on the use of group theory in general relativity theory.

There are twelve chapters in the book. The first six are devoted to rotation and Lorentz groups, and their representations. They include the spinor representation as well as the infinite-dimensional representations. The other six chapters deal with the application of groups -- particularly the Lorentz and the SL(2, C) groups -- to the theory of general relativity. Each chapter is concluded with a set of problems.

The topics covered range from the fundamentals of general relativity theory, its formulation as an SL(2, C) gauge theory, to exact solutions of the Einstein gravitational field equations. The important Bondi-Metzner-Sachs group, and its representations, conclude the book The entire book is self-contained in both group theory and general relativity theory, and no prior knowledge of either is assumed.

The subject of this book constitutes a relevant link between field theoreticians and general relativity theoreticians, who usually work rather independently of each other. The treatise is highly topical and of real interest to theoretical physicists, general relativists and applied mathematicians. It is invaluable to graduate students and research workers in quantum field theory, general relativity and elementary particle theory.

Gravitational waves (GWs) are a hot topic and promise to play a central role in astrophysics, cosmology, and theoretical physics. Technological developments have led us to the brink of their direct observation, which could become a reality in the coming years. The direct observation of GWs will open an entirely new field: GW astronomy. This is expected to bring a revolution in our knowledge of the universe by allowing the observation of previously unseen phenomena, such as the coalescence of compact objects (neutron stars and black holes), the fall of stars into supermassive black holes, stellar core collapses, big-bang relics, and the new and unexpected.
With a wide range of contributions by leading scientists in the field, Gravitational Waves covers topics such as the basics of GWs, various advanced topics, GW detectors, astrophysics of GW sources, numerical applications, and several recent theoretical developments. The material is written at a level suitable for postgraduate students entering the field.

This book explores the use of waves on strings and sound waves to illustrate the behaviour of waves. It shows how Albert Einstein overturned Newtonian physics and predicted startling new effects such as time dilation and length contraction for objects travelling at close to the speed of light.

What is Time? Assuming no prior specialized knowledge by the reader, the book raises specific, hitherto overlooked questions about how time works, such as how and why anyone can be made to be, at the very same instant, simultaneous with events that are actually days apart. It examines abiding issues in the physics of time or at its periphery which still elude a full explanation such as delayed choice experiments, the brain's perception of time during saccadic masking, and more and suggests that these phenomena can only exist because they ultimately obey applicable mathematics, thereby agreeing with a modern view that the universe and everything within it, including the mind, are ultimately mathematical structures. It delves into how a number of conundrums, such as the weak Anthropic Principle, could be resolved, and how such resolutions could be tested experimentally. All its various threads converge towards a same new vision of the ultimate essence of time, seen as a side effect from a deeper reality.

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 is the second volume of textbooks on atomic, molecular and optical physics, aiming at a comprehensive presentation of this highly productive branch of modern physics as an indispensable basis for many areas in physics and chemistry as well as in state of the art bio- and material-sciences. It primarily addresses advanced students (including PhD students), but in a number of selected subject areas the reader is lead up to the frontiers of present research. Thus even the active scientist is addressed. This volume 2 introduces lasers and quantum optics, while the main focus is on the structure of molecules and their spectroscopy, as well as on collision physics as the continuum counterpart to bound molecular states. The emphasis is always on the experiment and its interpretation, while the necessary theory is introduced from this perspective in a compact and occasionally somewhat heuristic manner, easy to follow even for beginners.

In a universe filled by chaos and disorder, one physicist makes the radical argument that the growth of order drives the passage of time -- and shapes the destiny of the universe. Time is among the universe's greatest mysteries. Why, when most laws of physics allow for it to flow forward and backward, does it only go forward? Physicists have long appealed to the second law of thermodynamics, held to predict the increase of disorder in the universe, to explain this. In The Janus Point, physicist Julian Barbour argues that the second law has been misapplied and that the growth of order determines how we experience time. In his view, the big bang becomes the "Janus point," a moment of minimal order from which time could flow, and order increase, in two directions. The Janus Point has remarkable implications: while most physicists predict that the universe will become mired in disorder, Barbour sees the possibility that order -- the stuff of life -- can grow without bound. A major new work of physics, The Janus Point will transform our understanding of the nature of existence.

This book is divided into two parts. In the first part we introduce the foundations of special relativity, such as, the inertial frame of reference, the definition of simulataneity, and Einstein's two basic hypotheses. We give the main relativistic effects, e.g. the relativity of simultaneity, velocity addition, length-contraction, the apparent shape of a moving body, time-dilation, Doppler effect, and the Thomas precession, In particular, the simultaneity problem and slow transport of clocks are investigated in detail by means of the test theories of special relativity. In the second part, variant types of experiments performed up to now are analyzed and compared to the predictions of special relativity. This shows that the experiments are a test of the two-way speed of light, but not of the one-way speed of light.

"The theory of relativity is not merely a scientific development of great importance in its own right. It is even more significant as the first stage of a radical change in our basic concepts, which began in physics, and which is spreading into other fields of science, and indeed, even into a great deal of thinking outside of science."
The opening lines of "The Special Theory of Relativity" show us David Bohm's unique ability to bridge the worlds of theoretical physics and the conceptual issues that underly science that gives his writing meaning far beyond the scientific community.
Based on his famous final year undergraduate lectures on theoretical physics at Birkbeck College, Bohm presents the theory of relativity as a unified whole, making clear the reasons which led to its adoption, and explaining its basic meaning. With clarity and grace, he also reveals the limited truth of some of the "common sense" assumptions which make it difficult for us to appreciate its full implications.

Bridging the gap between modern differential geometry and the mathematical physics of general relativity, this text, in its second edition, includes new and expanded material on topics such as the instability of both geodesic completeness and geodesic incompleteness for general space-times, geodesic connectibility, the generic condition, the sectional curvature function in a neighbourhood of degenerate two-plane, and proof of the Lorentzian Splitting Theorem.;Five or more copies may be ordered by college or university stores at a special student price, available on request.

General Relativity provides an unusually broad survey of the current state of this field. Chapters on mathematical relativity cover many topics, including initial value problems, a new approach to the partial differential equations of physics, and work on exact solutions. The chapters on relativistic cosmology and black holes explore cosmology. Other chapters deal with gravitational waves, experimental relativity, quantum gravity, and aspects of computing in relativity. The book will be useful both to postgraduates and to established workers in the field.

In this third volume of three, quantum electrodynamics is formulated in the language of physical "dressed" particles. A theory where charged particles interact via instantaneous action-at-a-distance forces is constructed - without need for renormalization. This theory describes electromagnetic phenomena in terms of directly interacting charges, but in full accord with fundamental principles of relativity and causality. Contents Three ways to look at QFT Dressing What are advantages of dressed Hamiltonian? Coulomb potential and beyond Decays RQD in higher orders Classical electrodynamics Experimental support of RQD Particles and relativity Special theory of relativity Unitary dressing transformation Integral for decay law Coulomb scattering integral in fourth order Relativistic invariance of Coulomb-Darwin-Breit electrodynamics

This second volume of three on relativistic quantum theories of interacting charged particles discusses quantum theories of systems with variable numbers of particles. Basics of the Fock space and quantum electrodynamics are covered with an emphasis on renormalization. In contrast to the usual treatment of the topic, particles (rather than fields) are chosen as basic ingredients. Contents Fock space Scattering in Fock space Quantum electrodynamics Renormalization Useful integrals Quantum fields of fermions Quantum field of photons QED interaction in terms of particle operators Relativistic invariance of QFT Loop integrals in QED Scattering matrix in (v/c)2 approximation Checks of physical dimensions

This book introduces notation, terminology, and basic ideas of relativistic quantum theories. The discussion proceeds systematically from the principle of relativity and postulates of quantum logics to the construction of Poincare invariant few-particle models of interaction and scattering. It is the first of three volumes formulating a consistent relativistic quantum theory of interacting charged particles. Contents Quantum logic Poincare group Quantum mechanics and relativity Observables Elementary particles Interaction Scattering Delta function Groups and vector spaces Group of rotations Lie groups and Lie algebras Hilbert space Operators Subspaces and projections Representations of groups and algebras Pseudo-orthogonal representation of Lorentz group