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.

Einstein's general theory of relativity is introduced in this advanced undergraduate and beginning graduate level textbook. Topics include special relativity, in the formalism of Minkowski's four-dimensional space-time, the principle of equivalence, Riemannian geometry and tensor analysis, Einstein field equation, as well as many modern cosmological subjects, from primordial inflation and cosmic microwave anisotropy to the dark energy that propels an accelerating universe.
The author presents the subject with an emphasis on physical examples and simple applications without the full tensor apparatus. The reader first learns how to describe curved spacetime. At this mathematically more accessible level, the reader can already study the many interesting phenomena such as gravitational lensing, precession of Mercury's perihelion, black holes, and cosmology. The full tensor formulation is presented later, when the Einstein equation is solved for a few symmetric cases. Many modern topics in cosmology are discussed in this book: from inflation, cosmic microwave anisotropy to the "dark energy" that propels an accelerating universe.
Mathematical accessibility, together with the various pedagogical devices (e.g., worked-out solutions of chapter-end problems), make it practical for interested readers to use the book to study general relativity and cosmology on their own.

REFLECTIONS ON SPACETIME - FOUNDATIONS, PHILOSOPHY AND HISTORY During the academic year 1992/93, an interdisciplinary research group constituted itself at the Zentrum fUr interdisziplinare Forschung (ZiF) in Bielefeld, Germany, under the title 'Semantical Aspects of Spacetime Theories', in which philosophers and physicists worked on topics in the interpretation and history of relativity theory. The present issue consists of contributions resulting from material presented and discussed in the group during the course of that year. The scope of the papers ranges from rather specialised issues arising from general relativity such as the problem of referential indeterminacy, to foundational questions regarding spacetime in the work of Carnap, Weyl and Hilbert. It is well known that the General Theory of Relativity (GTR) admits spacetime models which are 'exotic' in the sense that observers could travel into their own past. This poses a number of problems for the physical interpretation of GTR which are also relevant in the philosophy of spacetime. It is not enough to exclude these exotic models simply by stating that we live in a non-exotic universe, because it might be possible to "operate time machines" by actively changing the topology of the future part of spacetime. In his contribution, Earman first reviews the attempts of physicists to prove "chronology protection theorems" (CPTs) which exclude the operation of time machines under reasonable assumptions.

This book introduces the modern field of 3+1 numerical relativity. The book has been written in a way as to be as self-contained as possible, and only assumes a basic knowledge of special relativity. Starting from a brief introduction to general relativity, it discusses the different concepts and tools necessary for the fully consistent numerical simulation of relativistic astrophysical systems, with strong and dynamical gravitational fields. Among the topics discussed in detail are the following; the initial data problem, hyperbolic reductions of the field equations, guage conditions, the evolution of black hole space-times, relativistic hydrodynamics, gravitational wave extraction and numerical methods. There is also a final chapter with examples of some simple numerical space-times. The book is aimed at both graduate students and researchers in physics and astrophysics, and at those interested in relativistic astrophysics.

This thesis studies various aspects of non-critical strings both as an example of a non-trivial and solvable model of quantum gravity and as a consistent approximation to the confining flux tube in quantum chromodynamics (QCD). It proposes and develops a new technique for calculating the finite volume spectrum of confining flux tubes. This technique is based on approximate integrability and it played a game-changing role in the study of confining strings. Previously, a theoretical interpretation of available high quality lattice data was impossible, because the conventional perturbative expansion for calculating the string spectra was badly asymptotically diverging in the regime accessible on the lattice. With the new approach, energy levels can be calculated for much shorter flux tubes than was previously possible, allowing for a quantitative comparison with existing lattice data. The improved theoretical control makes it manifest that existing lattice data provides strong evidence for a new pseudoscalar particle localized on the QCD fluxtube - the worldsheet axion. The new technique paves a novel and promising path towards understanding the dynamics of quark confinement.

This book tells the story of how, over the past century, dedicated observers and pioneering scientists achieved our current understanding of the universe. It was in antiquity that humankind first attempted to explain the universe often with the help of myths and legends. This book, however, focuses on the time when cosmology finally became a true science. As the reader will learn, this was a slow process, extending over a large part of the 20th century and involving many astronomers, cosmologists and theoretical physicists. The book explains how empirical astronomical data (e.g., Leavitt, Slipher and Hubble) were reconciled with Einstein's general relativity; a challenge which finally led Friedmann, De Sitter and Lemaitre, and eventually Einstein himself, to a consistent understanding of the observational results. The reader will realize the extraordinary implications of these achievements and how deeply they changed our vision of the cosmos: From being small, static, immutable and eternal, it became vast and dynamical - originating from (almost) nothing, and yet now, nearly 14 billion years later, undergoing accelerated expansion. But, as always happens, as well as precious knowledge, new mysteries have also been created where previously absolute certainty had reigned.

This thesis describes the application of state-of-the-art high-energy X-ray studies to the astronomical quest for understanding obscured active galactic nuclei (AGN). These AGN are supermassive black holes growing by accretion of matter located in the nuclei of galaxies. The material that feeds these black holes also obscures them from view, rendering them challenging to study. It is possible to study them by effectively 'X-raying' galactic nuclei to peer through these obscuring veils. Beginning with the proof-of-concept application of novel X-ray Monte Carlo codes to the Nuclear Spectroscopic Telescope ARray (NuSTAR) spectrum of a known heavily obscured AGN, the thesis establishes the relevant parameters that characterise the AGN spectrum and central black hole growth rate. Next the largest sample of known heavily obscured AGN is compiled, finding the strength of a prominent iron spectral feature to weaken with AGN power. This is puzzling, and suggests that there may be more hidden AGN than previously thought. Finally by combining an all-sky infrared selection with NuSTAR follow-up, new heavily obscured AGN are identified. Obscuration emits infrared radiation, meaning that the infrared-selected AGN catalogue should be representative of the underlying AGN population. The absence of such representative catalogues has continually plagued cosmological studies, and the resultant obscured AGN fraction will be strongly constraining for AGN models.

These peer-reviewed NIC XV conference proceedings present the latest major advances in nuclear physics, astrophysics, astronomy, cosmochemistry and neutrino physics, which provide the necessary framework for a microscopic understanding of astrophysical processes. The book also discusses future directions and perspectives in the various fields of nuclear astrophysics research. In addition, it also includes a limited number of section of more general interest on double beta decay and dark matter.

The book employs oscillatory dynamical systems to represent the Universe mathematically via constructing classical and quantum theory of damped oscillators. It further discusses isotropic and homogeneous metrics in the Friedman-Robertson-Walker Universe and shows their equivalence to non-stationary oscillators. The wide class of exactly solvable damped oscillator models with variable parameters is associated with classical special functions of mathematical physics. Combining principles with observations in an easy to follow way, it inspires further thinking for mathematicians and physicists. Contents Part I: Dissipative geometry and general relativity theory Pseudo-Riemannian geometry and general relativity Dynamics of universe models Anisotropic and homogeneous universe models Metric waves in a nonstationary universe and dissipative oscillator Bosonic and fermionic models of a Friedman-Robertson-Walker universe Time dependent constants in an oscillatory universe Part II: Variational principle for time dependent oscillations and dissipations Lagrangian and Hamilton descriptions Damped oscillator: classical and quantum theory Sturm-Liouville problem as a damped oscillator with time dependent damping and frequency Riccati representation of time dependent damped oscillators Quantization of the harmonic oscillator with time dependent parameters

This book provides an introduction to the theory of relativity and the mathematics used in its processes. Three elements of the book make it stand apart from previously published books on the theory of relativity.
First, the book starts at a lower mathematical level than standard books with tensor calculus of sufficient maturity to make it possible to give detailed calculations of relativistic predictions of practical experiments. Self-contained introductions are given, for example vector calculus, differential calculus and integrations. Second, in-between calculations have been included, making it possible for the non-technical reader to follow step-by-step calculations. Thirdly, the conceptual development is gradual and rigorous in order to provide the inexperienced reader with a philosophically satisfying understanding of the theory.
The goal of this book is to provide the reader with a sound conceptual understanding of both the special and general theories of relativity, and gain an insight into how the mathematics of the theory can be utilized to calculate relativistic effects.

Astronomy in the Inca Empire was a robust and fundamental practice. The subsequent Spanish conquest of the Andes region disrupted much of this indigenous culture and resulted in a significant loss of information about its rich history. Through modern archaeoastronomy, this book helps recover and interpret some of these elements of Inca civilization. Astronomy was intricately woven into the very fabric of Andean existence and daily life. Accordingly, the text takes a holistic approach to its research, considering first and foremost the cultural context of each astronomy-related site. The chapters necessarily start with a history of the Incas from the beginning of their empire through the completion of the conquest by Spain before diving into an astronomical and cultural analysis of many of the huacas found in the heart of the Inca Empire. Over 300 color images-original artwork and many photos captured during the author's extensive field research in Machu Picchu, the Sacred Valley, Cusco, and elsewhere-are included throughout the book, adding visual insight to a rigorous examination of Inca astronomical sites and history.

This book presents an alternative representation of Einstein's Special Theory of Relativity, which makes Special Relativity much more comprehensible. Moreover, one will come across a fundamental relationship between the Special Theory of Relativity and the mechanics of space lattice. In all previous formulations, the Einsteinian special principle of relativity, in one or the other form is used as the starting point for Special Relativity. In correspondence to this principle, one takes it as granted apriori, that all observers independent of their uniform motion to each other measure one and the same propagation velocity of a light signal. This book is thought of as a lecture for physicists, mathematicians and computer scientists and concentrates on the students of these fields. The book should reach a broad circle of interested readers from the fields of natural sciences and philosophy and provide and invigorating experience for engineers.

These documents do nothing less than bear witness to one of the most dramatic changes in the foundations of science. The book has three sections that cover general relativity, epistemological issues, and quantum mechanics. This fascinating work will be a vital text for historians and philosophers of physics, as well as researchers in related physical theories.

Our vast Universe is filled with an enormous amount of matter and energy, which are the source of large gravitational potentials affecting all physical phenomena. Because this fact about the size and contents of the Universe was not known when our fundamental theories of dynamics and relativity were completed by the 1920s, the current theories - based as they are in empty space - fail to incorporate cosmic gravity. Though the current theories are consistent with the majority of empirical facts, there are some crucial discrepancies, which demand a drastic shift to a cosmic gravitational paradigm for the theories of relativity and dynamics. The book is a detailed and widely accessible account of this paradigm, called Cosmic Relativity, supported by ample empirical evidence. It is established that all motional relativistic effects are cosmic gravitational effects. The new theory of Cosmic Relativity solves and answers all outstanding questions and puzzles about dynamics and relativity.

The De Gruyter Studies in Mathematical Physics are devoted to the publication of monographs and high-level texts in mathematical physics. They cover topics and methods in fields of current interest, with an emphasis on didactical presentation. The series will enable readers to understand, apply and develop further, with sufficient rigor, mathematical methods to given problems in physics. For this reason, works with a few authors are preferred over edited volumes. The works in this series are aimed at advanced students and researchers in mathematical and theoretical physics. They can also serve as secondary reading for lectures and seminars at advanced levels.

The Golden Oldies series of the journal General Relativity and Gravitation reprints important papers in general relativity theory that were published 30 or more years ago and are either hard to get hold of, or were originally printed in a language other than English. They play a key part in making these important papers readily accessible today, in the language that has now become the lingua franca of scientific publication. The value of this reprinting is enhanced by an accompanying editorial note for each paper, which briefly explains the significance of the work and where it has subsequently led to, together with a biographical note about the author or authors. This volume presents a selection of 14 rarities among the Golden Oldies grouped in the three categories "Basic results in differential geometry and general relativity," "Discussion of physical effects" and "Basic exact solutions and their interpretation." Researchers in the field will appreciate having these important papers collected in one book for the first time. Reprinted from the journal General Relativity and Gravitation.

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.

'Dark energy' is the name given to the unknown cause of the Universe's accelerating expansion, which is one of the most significant and surprising discoveries in recent cosmology. Understanding this enigmatic ingredient of the Universe and its gravitational effects is a very active, and growing, field of research. In this volume, twelve world-leading authorities on the subject present the basic theoretical models that could explain dark energy, and the observational and experimental techniques employed to measure it. Covering the topic from its origin, through recent developments, to its future perspectives, this book provides a complete and comprehensive introduction to dark energy for a range of readers. It is ideal for physics graduate students who have just entered the field and researchers seeking an authoritative reference on the topic.

This detailed account of the controversy surrounding the publication of Albert Einstein's theory of relativity explores the ferocious popular and academic opposition which at one time encircled one of the most important scientific breakthroughs of the twentieth century. Based on extensive archival research, this fascinating discourse includes a compelling and entertaining examination of the contemporary literature created by Einstein's detractors. Exploring the arguments and strategies, social contexts, and motivations of Einstein's detractors, and providing unique insights into the dynamics of scientific controversies, this book is ideal for anyone interested in the history and philosophy of physics, popular science, and the public understanding of science.

This contributed volume explores the renaissance of general relativity after World War II, when it transformed from a marginal theory into a cornerstone of modern physics. Chapters explore key historical processes related to the theory of general relativity, in addition to presenting a thorough treatment of the relevant science behind these episodes. A broad historiographical framework is introduced first, thus providing the broad context in which the given computational approaches and case studies occurred. Written by an international and interdisciplinary group of expert authors, these chapters will bring readers to a more complete understanding of Einstein's theory. Specific topics include: Social and citation networks The Fock-Infeld dispute Wheeler's turn to gravitation theory The position of general relativity in theories of fundamental interactions The pursuit of a quantum theory of gravity The emergence of dark matter in relation to cosmological models Institutional frameworks for gravitational wave search in Europe The Renaissance of General Relativity in Context is ideal for historians, philosophers, and sociologists of science. Students and researchers in physics will also be interested in the topics explored.

In this book, leading theorists present new contributions and reviews addressing longstanding challenges and ongoing progress in spacetime physics. In the anniversary year of Einstein's General Theory of Relativity, developed 100 years ago, this collection reflects the subsequent and continuing fruitful development of spacetime theories. The volume is published in honour of Carl Brans on the occasion of his 80th birthday. Carl H. Brans, who also contributes personally, is a creative and independent researcher and one of the founders of the scalar-tensor theory, also known as Jordan-Brans-Dicke theory. In the present book, much space is devoted to scalar-tensor theories. Since the beginning of the 1990s, Brans has worked on new models of spacetime, collectively known as exotic smoothness, a field largely established by him. In this Festschrift, one finds an outstanding and unique collection of articles about exotic smoothness. Also featured are Bell's inequality and Mach's principle. Personal memories and historical aspects round off the collection.

This book is an elaboration of lecture notes for the graduate course on General Rela tivity given by the author at Boston University in the spring semester of 1972. It is an introduction to the subject only, as the time available for the course was limited. The author of an introduction to General Relativity is faced from the beginning with the difficult task of choosing which material to include. A general criterion as sisting in this choice is provided by the didactic character of the book: Those chapters have to be included in priority, which will be most useful to the reader in enabling him to understand the methods used in General Relativity, the results obtained so far and possibly the problems still to be solved. This criterion is not sufficient to ensure a unique choice. General Relativity has developed to such a degree, that it is impossible to include in an introductory textbook of a reasonable length even a very condensed treatment of all important problems which have been discussed until now and the author is obliged to decide, in a more or less subjective manner, which of the more recent developments to omit. The following lines indicate by means of some examples the kind of choice made in this book."

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.

Our esteemed colleague C. V. Vishveshwara, popularly known as Vishu, turned sixty on 6th March 1998. His colleagues and well wishers felt that it would be appropriate to celebrate the occasion by bringing out a volume in his honour. Those of us who have had the good fortune to know Vishu, know that he is unique, in a class by himself. Having been given the privilege to be the volume's editors, we felt that we should attempt something different in this endeavour. Vishu is one of the well known relativists from India whose pioneer ing contributions to the studies of black holes is universally recognised. He was a student of Charles Misner. His Ph. D. thesis on the stability of the Schwarzschild black hole, coordinate invariant characterisation of the sta tionary limit and event horizon for Kerr black holes and subsequent seminal work on quasi-normal modes of black holes have passed on to become the starting points for detailed mathematical investigations on the nature of black holes. He later worked on other aspects related to black holes and compact objects. Many of these topics have matured over the last thirty years. New facets have also developed and become current areas of vigorous research interest. No longer are black holes, ultracompact objects or event horizons mere idealisations of mathematical physicists but concrete entities that astrophysicists detect, measure and look for. Astrophysical evidence is mounting up steadily for black holes."