The purpose of this book is to illustrate some of the most important techniques which are helpful in combinatorial problems when computing quantum effects in covariant theories, like general relativity. In fact, most of the techniques find application also in broader contexts, such as low energy effective (chiral) Lagrangians or even in specific problems in condensed matter. Some of the topics covered are: the background field approach and the heat kernel ideas. The arguments are explained in some detail and the presentation is meant for young researchers and advanced students who are starting working in the field. As prerequisite the reader should have attended a course in quantum field theory including Feynman's path integral. In the Appendix a nontrivial calculation of one-loop divergences in Einstein-Hilbert gravity is explained step-by-step.

Essential mathematical insights into one of the most important and challenging open problems in general relativity—the stability of black holes One of the major outstanding questions about black holes is whether they remain stable when subject to small perturbations. An affirmative answer to this question would provide strong theoretical support for the physical reality of black holes. In this book, Sergiu Klainerman and Jérémie Szeftel take a first important step toward solving the fundamental black hole stability problem in general relativity by establishing the stability of nonrotating black holes—or Schwarzschild spacetimes—under so-called polarized perturbations. This restriction ensures that the final state of evolution is itself a Schwarzschild space. Building on the remarkable advances made in the past fifteen years in establishing quantitative linear stability, Klainerman and Szeftel introduce a series of new ideas to deal with the strongly nonlinear, covariant features of the Einstein equations. Most preeminent among them is the general covariant modulation (GCM) procedure that allows them to determine the center of mass frame and the mass of the final black hole state. Essential reading for mathematicians and physicists alike, this book introduces a rich theoretical framework relevant to situations such as the full setting of the Kerr stability conjecture.

Based on lectures given at a summer school on computer algebra, the book provides a didactic description of the facilities available in three computor algebra systems - MAPLE, REDUCE and SHEEP - for performing calculations in the algebra-intensive field of general relativity. With MAPLE and REDUCE, two widespread great-purpose systems, the reader is shown how to use currently available packages to perform calculations with respect to tetrads, co-ordinate systems, and Poincare` gauge theory. The section on SHEEP and Stensor, being the first published book on these systems, explains how to use these systems to tackle a wide range of calculations with respect to tackle a wide range of calculations in general relativity, including the manipulation of indicial formulae. For the researcher in general relativity, the book therefore promises a wide overview of the facilities available in computer algebra to lessen the burden of the lengthy, error-prone calculations involved in their research.

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.

Starting out from humankind's earliest ideas about the cosmos, this book gives the reader a clear overview of our current understanding of the universe, including big bang theories and the formation of stars and galaxies, as well as addressing open questions. The author shows how our present view gradually developed from observations, and also how the outcome of ongoing research may still change this view. The book brings together concepts in physics and astronomy, including some history in both cases. The text is descriptive rather than technical: the goal is to present things rigorously and without oversimplification, by highlighting the crucial physical concepts. The only prerequisite is a qualitative knowledge of basic physics concepts at high-school level.

Of all philosophers of the 20th century, few built more bridges between academic disciplines than Karl Popper. He contributed to a wide variety of fields in addition to the epistemology and the theory of scientific method for which he is best known. This book illustrates and evaluates the impact, both substantive and methodological, that Popper has had in the natural and mathematical sciences. The topics selected include quantum mechanics, evolutionary biology, cosmology, mathematical logic, statistics, and cognitive science. The approach is multidisciplinary, opening a dialogue across scientific disciplines and between scientists and philosophers.

Offers an accessible text and reference (a cosmic-ray manual) for graduate students entering the field and high-energy astrophysicists will find this an accessible cosmic-ray manual Easy to read for the general astronomer, the first part describes the standard model of cosmic rays based on our understanding of modern particle physics. Presents the acceleration scenario in some detail in supernovae explosions as well as in the passage of cosmic rays through the Galaxy. Compares experimental data in the atmosphere as well as underground are compared with theoretical models

Deep within galaxies like the Milky Way, astronomers have found a fascinating legacy of Einstein's general theory of relativity: supermassive black holes. Connected to the evolution of the galaxies that contain these black holes, galactic nuclei are the sites of uniquely energetic events, including quasars, stellar tidal disruptions, and the generation of gravitational waves. This textbook is the first comprehensive introduction to dynamical processes occurring in the vicinity of supermassive black holes in their galactic environment. Filling a critical gap, it is an authoritative resource for astrophysics and physics graduate students, and researchers focusing on galactic nuclei, the astrophysics of massive black holes, galactic dynamics, and gravitational wave detection. It is an ideal text for an advanced graduate-level course on galactic nuclei and as supplementary reading in graduate-level courses on high-energy astrophysics and galactic dynamics.

David Merritt summarizes the theoretical work of the last three decades on the evolution of galactic nuclei, the formation of massive black holes, and the interaction between black holes and stars. He explores in depth such important topics as observations of galactic nuclei, dynamical models, weighing black holes, motion near supermassive black holes, evolution of nuclei due to gravitational encounters, loss cone theory, and binary supermassive black holes. Self-contained and up-to-date, the textbook includes a summary of the current literature and previously unpublished work by the author.

For researchers working on active galactic nuclei, galaxy evolution, and the generation of gravitational waves, this book will be an essential resource.

This thesis provides a comprehensive view of the physics of charmed hadrons in high-energy proton-proton and heavy-ion collisions. Given their large masses, charm quarks are produced in the early stage of a heavy-ion collision and they subsequently experience the full system evolution probing the colour-deconfined medium called quark-gluon plasma (QGP) created in such collisions. In this thesis, the mechanisms of charm-quark in-medium energy loss and hadronisation are discussed via the measurements of the production of charm mesons with (Ds+) and without (D+) strange-quark content in different colliding systems, using data collected by the ALICE experiment at the CERN LHC. The participation of the charm quark and its possible thermalisation in the QGP are studied via measurements of azimuthal anisotropies in the production of D+ mesons. Finally, the prospects for future measurements with the upgraded ALICE experimental apparatus and with more refined machine learning techniques are presented.

This book highlights the review of articles in theoretical physics by the students of Professor K. Babu Joseph, as a Festschrift for his 80th Birthday. This book is divided into four sections based on the contributions of Babu Joseph and his students. The four sections are Cosmology, High Energy Physics, Mathematical Physics and Non-linear Dynamics and its applications.

This book collates papers presented at two international conferences (held at the Australian National University in 2018 and Birkbeck College London in 2019) exploring the relationships between big history and astrobiology and their wider implications for society. These two relatively new academic disciplines aim to integrate human history with the wider history of the universe and the search for life elsewhere. The book will show that, despite differences in emphasis, big history and astrobiology share much in common, especially their interdisciplinary approaches and the cosmic and evolutionary perspectives that they both engender. Specifically, the book addresses the unified, all-embracing, nature of knowledge, the impact of big history on humanity and the world at large, the possible impact of SETI on astrobiology and big history, the cultural signature of Earth's inhabitants beyond our own planet, and the political implications of a planetary worldview. The principal readership is envisaged to comprise scholars working in the fields of astrobiology, big history and space exploration interested in forging interdisciplinary links between these diverse topics, together with educators, and a wider public, interested in the societal implications of the cosmic and evolutionary perspectives engendered by research in these fields.

To those of us who are not mathematicians or physicists, Einstein's theory of relativity often seems incomprehensible, exotic, and of little real-world use. None of this is true. Daniel F. Styer's introduction to the topic not only shows us why these beliefs are mistaken but also shines a bright light on the subject so that any curious-minded person with an understanding of algebra and geometry can both grasp and apply the theory.

Styer starts off slowly and proceeds carefully, explaining the concepts undergirding relativity in language comprehensible to nonscientists yet precise and accurate enough to satisfy the most demanding professional. He demonstrates how the theory applies to various real-life situations with easy equations and simple, clear diagrams. Styer's classroom-tested method of conveying the core ideas of relativity--the relationship among and between time, space, and motion and the behavior of light--encourages questions and shows the way to finding the answers. Each of the book's four parts builds on the sections that come before, leading the reader by turn through an overview of foundational ideas such as frames of reference, revelatory examples of time dilation and its attendant principles, an example-based exploration of relativity, and explanations of how and why gravity and spacetime are linked. By demonstrating relativity with practical applications, Styer teaches us to truly understand and appreciate its importance, beauty, and usefulness.

Featuring worked and end-of-chapter problems and illustrated, nontechnical explanations of core concepts, while dotted throughout with questions and answers, puzzles, and paradoxes, "Relativity for the Questioning Mind" is an enjoyable-to-read, complete, concise introduction to one of the most important scientific theories yet discovered. The appendixes provide helpful hints, basic answers to the sample problems, and materials to stimulate further exploration.

This book presents Special Relativity in a language accessible to students while avoiding the burdens of geometry, tensor calculus, space-time symmetries, and the introduction of four vectors. The search for clarity in the fundamental questions about Relativity, the discussion of historical developments before and after 1905, the strong connection to current research topics, many solved examples and problems, and illustrations of the material in colloquial discussions are the most significant and original assets of this book. Importantly for first-time students, Special Relativity is presented such that nothing needs to be called paradoxical or apparent; everything is explained. The content of this volume develops and builds on the book Relativity Matters (Springer, 2017). However, this presentation of Special Relativity does not require 4-vector tools. The relevant material has been extended and reformulated, with additional examples and clarifications. This introduction of Special Relativity offers conceptual insights reaching well beyond the usual method of teaching relativity. It considers relevant developments after the discovery of General Relativity (which itself is not presented), and advances the reader into contemporary research fields. This presentation of Special Relativity is connected to present day research topics in particle, nuclear, and high intensity pulsed laser physics and is complemented by the current cosmological perspective. The conceptual reach of Special Relativity today extends significantly further compared even to a few decades ago. As the book progresses, the qualitative and historical introduction turns into a textbook-style presentation with many detailed results derived in an explicit manner. The reader reaching the end of this text needs knowledge of classical mechanics, a good command of elementary algebra, basic knowledge of calculus, and introductory know-how of electromagnetism.

This book presents the superfield description of various supersymmetric field theory models in three- and four-dimensional space-times. A mapping between superfield and component formulations of supersymmetric field theories is discussed. The author also describes the methodology for calculating quantum corrections in these theories employing supergraph formalism and functional methods, and illustrates these approaches with many detailed examples of how such calculations are performed for various superfield models.

This textbook introduces the special theory of relativity at a level which is accessible to undergraduate students and even high school students with a strong foundation in algebra. The presentation emphasizes clean algebraic and geometrical methods, visualized with plenty of illustrations, resulting in a textbook that is modern and serious yet accessible. Replete with many solved exercises and copious spacetime diagrams, this book will help students develop relativistic intuition when encountering the subject for the first time. The emphasis on geometric methods, combined with the pedagogically appealing k-calculus approach, makes this book ideal for a self-contained course on special relativity or as supplementary reading for modern physics courses. It will also appeal to high schoolers with a strong math background who want to get ahead.

Presenting the history of space-time physics, from Newton to Einstein, as a philosophical development DiSalle reflects our increasing understanding of the connections between ideas of space and time and our physical knowledge. He suggests that philosophy's greatest impact on physics has come about, less by the influence of philosophical hypotheses, than by the philosophical analysis of concepts of space, time and motion, and the roles they play in our assumptions about physical objects and physical measurements. This way of thinking leads to interpretations of the work of Newton and Einstein and the connections between them. It also offers ways of looking at old questions about a priori knowledge, the physical interpretation of mathematics, and the nature of conceptual change. Understanding Space-Time will interest readers in philosophy, history and philosophy of science, and physics, as well as readers interested in the relations between physics and philosophy.

This book aims to span the cultural differences separating the humanities from the natural sciences. In his exposition, the author goes well beyond the typical level found in popular science presentations. There is a separate chapter devoted to the mathematical fundamentals needed for understanding many concepts in physics.

These two volumes are the proceedings of a major International Symposium on General Relativity held at the University of Maryland 27 to 29 March 1993 to celebrate the sixtieth birthdays of Professor Charles Misner and Professor Dieter Brill. The volumes cover classical general relativity, quantum gravity and quantum cosmology, canonical formulation and the initial value problem, topology and geometry of spacetime and fields, mathematical and physical cosmology, and Black Hole physics and astrophysics. As invited articles, the papers in these volumes have an aim which goes beyond that of a standard conference proceedings. Not only do the authors discuss the most recent research results in their fields, but many also provide historical perspectives on how their subjects developed and offer individual insights in their search for new directions.

This volume contains the proceedings of the twelfth triannual International Conference on General Relativity and Gravitation, the premier conference for presentation and discussion of new ideas in relativity and cosmology. The volume will contain the invited talks as well as short reports on the parallel workshops that took place at the meeting. It will be essential reading for all research workers in relativity, cosmology and astrophysics.

The past forty years have been a time of spectacular development in the study of general relativity and cosmology. A special role in this has been played by the influential research groups led by Dennis Sciama in Cambridge, Oxford, and Trieste. In April 1992 many of his ex-students and collaborators came to Trieste (where he is currently Professor) for a review meeting to celebrate his 65th birthday. This book consists of written versions of the talks presented which, taken together, comprise an authoritative overview of developments which have taken place during his career to date. The topics covered include fundamental questions in general relativity and cosmology, black holes, active galactic nuclei, galactic structure, dark matter, and large scale structure.

This volume includes contributions by leading workers in the field given at the workshop on Numerical Relativity held in Southampton in December 1991. Numerical Relativity, or the numerical solution of astrophysical problems using powerful computers to solve Einstein's equations, has grown rapidly over the last 15 years. It is now an important route to understanding the structure of the Universe, and is the only route currently available for approaching certain important astrophysical scenarios. The Southampton meeting was notable for the first full report of the new 2+2 approach and the related null or characteristic approaches, as well as for updates on the established 3+1 approach, including both Newtonian and fully relativistic codes. The contributions range from theoretical (formalisms, existence theorems) to the computational (moving grids, multiquadrics and spectral methods).

In the late 20th and beginning 21st century high-precision astronomy, positioning and metrology strongly rely on general relativity. Supported by exercises and solutions this book offers graduate students and researchers entering those fields a self-contained and exhaustive but accessible treatment of applied general relativity. The book is written in a homogenous (graduate level textbook) style allowing the reader to understand the arguments step by step. It first introduces the mathematical and theoretical foundations of gravity theory and then concentrates on its general relativistic applications: clock rates, clock sychronization, establishment of time scales, astronomical references frames, relativistic astrometry, celestial mechanics and metrology. The authors present up-to-date relativistic models for applied techniques such as Satellite LASER Ranging (SLR), Lunar LASER Ranging (LLR), Globale Navigation Satellite Systems (GNSS), Very Large Baseline Interferometry (VLBI), radar measurements, gyroscopes and pulsar timing. A list of acronyms helps the reader keep an overview and a mathematical appendix provides required functions and terms.

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.

Explore spectacular advances in cosmology, relativistic astrophysics, gravitational wave science, mathematics, computational science, and the interface of gravitation and quantum physics with this unique celebration of the centennial of Einstein's discovery of general relativity. Twelve comprehensive and in-depth reviews, written by a team of world-leading international experts, together present an up-to-date overview of key topics at the frontiers of these areas, with particular emphasis on the significant developments of the last three decades. Interconnections with other fields of research are also highlighted, making this an invaluable resource for both new and experienced researchers. Commissioned by the International Society on General Relativity and Gravitation, and including accessible introductions to cutting-edge topics, ample references to original research papers, and informative colour figures, this is a definitive reference for researchers and graduate students in cosmology, relativity, and gravitational science.