Black holes are one of the most remarkable predictions of Einstein's general relativity. In recent years, ideas in brane-world cosmology, string theory and gauge/gravity duality have motivated studies of black holes in more than four dimensions, with surprising results. In higher dimensions, black holes exist with exotic shapes and unusual dynamics. Edited by leading expert Gary Horowitz, this exciting book is the first devoted to this new field. The major discoveries are explained by the people who made them: Rob Myers describes the Myers-Perry solutions that represent rotating black holes in higher dimensions; Ruth Gregory describes the Gregory-Laflamme instability of black strings; and Juan Maldacena introduces gauge/gravity duality, the remarkable correspondence that relates a gravitational theory to nongravitational physics. Accessible to anyone with a standard course in general relativity, this is an important resource for graduate students and researchers in general relativity, string theory and high energy physics.

This is a remarkable book: a symposium proceedings volume that will also function as a graduate-level text. Dedicated to the great theorist S. Chandrasekhar, the book consists of ten well-written chapters that cover the essential tools of theoretical astrophysics. The first half of the volume is concerned with the theory of how stars work (structure, stability, rotation, magnetism, dynamics) and the latter half is mainly a survey of relativistic astrophysics. . . . Read it for a broad-brush view of what theorists are up to now and how they solve problems.--Journal of the British Astronomical Association The book as a whole should be a gift from every research supervisor to every new graduate student in theoretical astronomy.--D. W. Sciama, Science

The book attempts to provide an introduction to quantum field theory emphasizing conceptual issues frequently neglected in more "utilitarian" treatments of the subject. The book is divided into four parts, entitled respectively "Origins", "Dynamics", "Symmetries", and "Scales". The emphasis is conceptual - the aim is to build the theory up systematically from some clearly stated foundational concepts - and therefore to a large extent anti-historical, but two historical Chapters ("Origins") are included to situate quantum field theory in the larger context of modern physical theories. The three remaining sections of the book follow a step by step reconstruction of this framework beginning with just a few basic assumptions: relativistic invariance, the basic principles of quantum mechanics, and the prohibition of physical action at a distance embodied in the clustering principle. The ``Dynamics" section of the book lays out the basic structure of quantum field theory arising from the sequential insertion of quantum-mechanical, relativistic and locality constraints. The central role of symmetries in relativistic quantum field theories is explored in the third section of the book, while in the final section, entitled "Scales", we explore in detail the feature of quantum field theories most critical for their enormous phenomenological success - the scale separation property embodied by the renormalization group properties of a theory defined by an effective local Lagrangian.The book includes a wide range of problems at chapter ends. Solutions can be requested via the publisher's web site.

Over the past years the author has developed a quantum language going beyond the concepts used by Bohr and Heisenberg. The simple formal algebraic language is designed to be consistent with quantum theory. It differs from natural languages in its epistemology, modal structure, logical connections, and copulatives. Starting from ideas of John von Neumann and in part also as a response to his fundamental work, the author bases his approach on what one really observes when studying quantum processes. This way the new language can be seen as a clue to a deeper understanding of the concepts of quantum physics, at the same time avoiding those paradoxes which arise when using natural languages. The work is organized didactically: The reader learns in fairly concrete form about the language and its structure as well as about its use for physics.

This 1985 book consists of essays reviewing progress or reporting original results in areas of the applications of gravity theory to which Professor Bonnor had contributed. In particular, the influence of his work in two important fields of interest to astonomers, physicists and mathematicians, galaxy formation and the study of axisymmetric solutions in general relativity, is well recognised. The essays on galaxies and astrophysical cosmology are related to Professor Bonnor's work on the treatment of perturbations of uniform cosmological models, while the essays on axisymmetric solutions reflect the concerns of his long series of papers on the subject, which began with generating techniques and went on to deal with interpretation of the solutions obtained. In addition there is a number of essays on other topics in gravity theory, including numerical work, mathematical cosmology and gravitational waves.

First published in 1989, this book is comprised of invited contributions from speakers at the international workshop, Frontiers in Numerical Relativity, held at the University of Illinois, Urbana-Champaign, in May 1988. Advances in supercomputer technology and computational algorithms have stimulated rapid progress in attempts to understand, through numerical means, such diverse phenomena as gravitational radiation emission from astrophysical sources, the evolution of inhomogenous cosmologies and its effects on nucleosynthesis, cosmic string interactions, the formation of 'naked singularities' and the cosmic censorship conjecture and the dynamics of black holes. The book should be of interest to researchers and graduate students in the field of general relativity, astrophysics and applied numerical analysis who wish to understand developments in computer studies of general relativity at the time of publication.

Alfred North Whitehead (1861-1947) was a prominent English mathematician and philosopher who co-authored the highly influential Principia Mathematica with Bertrand Russell. Originally published in 1922, this book forms the follow-up volume to The Principles of Natural Knowledge (1919) and The Concept of Nature (1920). In it, Whitehead puts forward an alternative theory of relativity, one which goes against the heterogeneity of Einstein's later theories in deducing that 'our experience requires and exhibits a basis in uniformity'. The text is divided into three parts - 'General Principles', 'Physical Applications', and 'Elementary Theory of Tensors' - and exhibits a characteristically ambitious approach in mixing various academic disciplines. This is a fascinating book that will be of value to anyone with an interest in natural science, physics, and philosophy, together with the history of science.

Following on from a previous volume on Special Relativity, Andrew Steane's second volume on General Relativity and Cosmology is aimed at advanced undergraduate or graduate students undertaking a physics course, and encourages them to expand their knowledge of Special Relativity. Beginning with a survey of the main ideas, the textbook goes on to give the methodological foundations to enable a working understanding of astronomy and gravitational waves (linearized approximation, differential geometry, covariant differentiation, physics in curved spacetime). It covers the generic properties of horizons and black holes, including Hawking radiation, introduces the key concepts in cosmology and gives a grounding in classical field theory, including spinors and the Dirac equation, and a Lagrangian approach to General Relativity. The textbook is designed for self-study and is aimed throughout at clarity, physical insight, and simplicity, presenting explanations and derivations in full, and providing many explicit examples.

Ebenezer Cunningham was a British mathematician and Cambridge graduate with an intense interest in the theory of special relativity, a subject that was just beginning to be recognised as he wrote. This book, first published by Cambridge University Press in 1914, was one of the first treatises in the English language to focus on special relativity. Its publication firmly established Cunningham as one of the greatest minds in the field. Within this volume, Cunningham firstly offers the reader a preface contextualising the progress of the study of relativity thus far. His chapters then process to relate relativity to existing physical theory, expanding on the relativity of Newtonian dynamics, electron theory and theories of Albert Einstein amongst others. This book is thoroughly and engagingly written, and promises to fascinate all those with an interest in the early study of special relativity.

One of the most of exciting aspects is the general relativity pred- tion of black holes and the Such Big Bang. predictions gained weight the theorems through Penrose. singularity pioneered In various by te- books on theorems general relativity singularity are and then presented used to that black holes exist and that the argue universe started with a To date what has big been is bang. a critical of what lacking analysis these theorems predict-' We of really give a proof a typical singul- theorem and this ity use theorem to illustrate problems arising through the of possibilities violations" and "causality weak "shell very crossing These singularities." add to the problems weight of view that the point theorems alone singularity are not sufficient to the existence of predict physical singularities. The mathematical theme of the book In order to both solid gain a of and intuition understanding good for any mathematical theory, one, should to realise it as model of try a a fam- iar non-mathematical theories have had concept. Physical an especially the important on of and impact development mathematics, conversely various modern theories physical rather require sophisticated mathem- ics for their formulation. both and mathematics Today, physics are so that it is often difficult complex to master the theories in both very s- in the of jects. However, case differential pseudo-Riemannian geometry or the general relativity between and mathematics relationship physics is and it is therefore especially close, to from interd- possible profit an ciplinary approach.

This book describes a paradigm change in modern physics from the philosophy and mathematical expression of the quantum theory to those of general relativity. The approach applies to all domains - from elementary particles to cosmology. The change is from the positivistic views in which atomism, nondeterminism and measurement are fundamental, to a holistic view in realism, wherein matter - electrons, galaxies, - are correlated modes of a single continuum, the universe. A field that unifies electromagnetism, gravity and inertia is demonstrated explicitly, with new predictions, in terms of quaternion and spinor field equations in a curved spacetime. Quantum mechanics emerges as a linear, flatspace approximation for the equations of inertia in general relativity.

The relation between quantum theory and the theory of gravitation remains one of the most outstanding unresolved issues of modern physics. According to general expectation, general relativity as well as quantum (field) theory in a fixed background spacetime cannot be fundamentally correct. Hence there should exist a broader theory comprising both in appropriate limits, i.e., quantum gravity. This book gives readers a comprehensive introduction accessible to interested non-experts to the main issues surrounding the search for quantum gravity. These issues relate to fundamental questions concerning the various formalisms of quantization; specific questions concerning concrete processes, like gravitational collapse or black-hole evaporation; and the all important question concerning the possibility of experimental tests of quantum-gravity effects.

Special and General Relativity are concisely developed together with essential aspects of nuclear and particle physics. Problem sets are provided for many chapters, making the book ideal for a course on the physics of white dwarf and neutron star interiors. Norman K. Glendenning is Senior Scientist Emeritus at the Nuclear Science Division, Institute for Nuclear and Particle Astrophysics, Lawrence Berkeley National Laboratory at the University of California, Berkeley. He is the author of numerous books.

Carl Friedrich von Weizsacker s "Aufbau der Physik," first published in 1985, was intended as an overview of his lifelong concern: an understanding of the unity of physics. That is, the idea of a quantum theory of binary alternatives (the so-called ur-theory), a unified quantum theoretical framework in which spinorial symmetry groups are considered to give rise to the structure of space and time.

The book saw numerous reprints, but it was published in German only.

The present edition, in English, provides a newly arranged and revised version, in which some original chapters and sections have been deleted, and a new chapter about further insights and results of ur-theoretic research of the late 1980 s and 1990 s, mainly by the work of Thomas Gornitz, has been included, as well as a general introduction to Weizsacker s Philosophy of Physics.

Carl Friedrich von Weizsacker also enjoys high esteem by a much broader audience for his socio-cultural, political and religious thoughts and writings. In him the intercultural and interdisciplinary dialogue has found one of its most important proponents: a great thinker who combines the perspectives of science, philosophy, religion and politics with a view towards the challenges as well as the responsibilities of our time."

Ever since its infancy, humankind has been seeking answers to some very basic and profound questions. Did the Universe begin? If it did, how old is it, and where did it come from? What is its shape? What is it made of? Fascinating myths and brilliant in- itions attempting to solve such enigmas can be found all through the history of human thought. Every culture has its own legends, itsownworldcreationtales, itsphilosophicalspeculations, itsre- gious beliefs. Modern science, however, cannot content itself with fanciful explanations, no matter how suggestive they are. No- days, our theories about the Universe, built upon rational ded- tion, have to survive the hard test of experiment and observation. Cosmology, the science which studies the origin and evo- tion of the Universe, had to overcome enormous dif?culties before it could achieve the same level of dignity as other physical dis- plines. At ?rst, it had no serious physical model and mathematical tools that could be used to address the complexity of the problems it had to face. Then, it suffered from a chronic lack of experim- tal data, which made it almost impossible to test the theoretical speculations. Given this situation, answering rigorously the many questions on the nature of the Universe seemed nothing more than a delusion. Today, however, things have changed. We live in the golden age of cosmology: an exciting moment, when, for the ?rst time, we are able to scienti?cally understand our Univers

This mathematically-oriented introduction takes the point of view that students should become familiar, at an early stage, with the physics of relativistic continua and thermodynamics within the framework of special relativity. Therefore, in addition to standard textbook topics such as relativistic kinematics and vacuum electrodynamics, the reader will be thoroughly introduced to relativistic continuum and fluid mechanics. There is emphasis on the 3+1 splitting technique.

Is time, even locally, like the real line? Multiple structures of time, implicit in physics, create a consistency problem. A tilt in the arrow of time is suggested as the most conservative hypothesis which provides approximate consistency within physics and with topology of mundane time. Mathematically, the assumed constancy of the velocity of light (needed to measure time) implies functional differential equations of motion, that have both retarded and advanced deviating arguments with the hypothesis of a tilt. The novel features of such equations lead to a nontrivial structure of time and quantum-mechanical behaviour. The entire argument is embedded in a pedagogical exposition which amplifies, corrects, and questions the conventionally accepted approach. The exposition includes historical details and explains, for instance, why the entropy law is inadequate for time asymmetry, and why notions such as time asymmetry (hence causality) may be conceptually inadequate. The first three parts of the book are especially suited as supplementary reading material for undergraduate and graduate students and teachers of physics. The new ideas are addressed to researchers in physics and philosophy of science concerned with relativity and the interpretation of quantum mechanics.

This book introduces the general theory of relativity and includes applications to cosmology. The book provides a thorough introduction to tensor calculus and curved manifolds. After the necessary mathematical tools are introduced, the authors offer a thorough presentation of the theory of relativity. Also included are some advanced topics not previously covered by textbooks, including Kaluza-Klein theory, Israel's formalism and branes. Anisotropic cosmological models are also included. The book contains a large number of new exercises and examples, each with separate headings. The reader will benefit from an updated introduction to general relativity including the most recent developments in cosmology.

This volume presents a selection of 434 letters from and to the Dutch physicist and Nobel Prize winner Hendrik Antoon Lorentz (1853-1928), covering the period from 1883 until a few months before his death in February 1928. The sheer size of the available correspondence (approximately 6000 letters from and to Lorentz) preclude a full publication. The letters included in this volume have been selected according to various criteria, the most important of which is scientific importance. A second criterion has been the availability of letters both from and to Lorentz, so that the reader can follow the exchange between Lorentz and his correspondent. Within such correspondences a few unimportant items, dealing with routine administrative or organizational matters, have been omitted. An exception to the scientific criterion is the exchange of letters between Lorentz and Albert Einstein, Max Planck, Woldemar Voigt, and Wilhelm Wien during World War I: these letters have been included because they shed important light on the disruption of the scientific relations during the war and on the political views of these correspondents as well as of Lorentz. similar reasons the letters exchanged with Einstein and Planck on post-war political issues have been included. Biographical sketch Hendrik Antoon Lorentz was born on July 18, 1853 in the Dutch town of Arnhem. He was the son of a relatively well-to-do owner of a nursery.

This volume is intended as a systematic introduction to gauge field theory for advanced undergraduate and graduate students in high energy physics. The discussion is restricted to the classical (non-quantum) theory in Minkowski spacetime. Particular attention has been given to conceptual aspects of field theory, accurate definitions of basic physical notions, and thorough analysis of exact solutions to the equations of motion for interacting systems.

The theory of relativity describes the laws of physics in a given space-time. However, a physical theory must provide observational predictions expressed in terms of measurements, which are the outcome of practical experiments and observations. Ideal for readers with a mathematical background and a basic knowledge of relativity, this book will help readers understand the physics behind the mathematical formalism of the theory of relativity. It explores the informative power of the theory of relativity, and highlights its uses in space physics, astrophysics and cosmology. Readers are given the tools to pick out from the mathematical formalism those quantities that have physical meaning and which can therefore be the result of a measurement. The book considers the complications that arise through the interpretation of a measurement, which is dependent on the observer who performs it. Specific examples of this are given to highlight the awkwardness of the problem.

It is commonly assumed that if the Sun suddenly turned into a black hole, it would suck Earth and the rest of the planets into oblivion. Yet, as prominent author and astrophysicist Jeffrey Bennett points out, black holes don't suck. With that simple idea in mind, Bennett begins an entertaining introduction to Einstein's theories of relativity, describing the amazing phenomena readers would actually experience if they took a trip to a black hole. The theory of relativity reveals the speed of light as the cosmic speed limit, the mind-bending ideas of time dilation and curvature of spacetime, and what may be the most famous equation in history: E = mc2. Indeed, the theory of relativity shapes much of our modern understanding of the universe. It is not "just a theory"-every major prediction of relativity has been tested to exquisite precision, and its practical applications include the Global Positioning System (GPS). Amply illustrated and written in clear, accessible prose, Bennett's book proves anyone can grasp the basics of Einstein's ideas. His intuitive, nonmathematical approach gives a wide audience its first real taste of how relativity works and why it is so important to science and the way we view ourselves as human beings.

Dark energy, the mysterious cause of the accelerating expansion of the universe, is one of the most important fields of research in astrophysics and cosmology today. Introducing the theoretical ideas, observational methods and results, this textbook is ideally suited to graduate courses on dark energy, and will also supplement advanced cosmology courses. Providing a thorough introduction to this exciting field, the textbook covers the cosmological constant, quintessence, k-essence, perfect fluid models, extra-dimensional models, and modified gravity. Observational research is reviewed, from the cosmic microwave background to baryon acoustic oscillations, weak lensing and cluster abundances. Every chapter ends with problems, with full solutions provided, and any calculations are worked through step-by-step.