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Singularity Theory and Gravitational Lensing by Arlie O. Petters,Harold Levine,Joachim Wambsganss Pdf
This monograph is the first to develop a mathematical theory of gravitational lensing. The theory applies to any finite number of deflector planes and highlights the distinctions between single and multiple plane lensing. Introductory material in Parts I and II present historical highlights and the astrophysical aspects of the subject. Part III employs the ideas and results of singularity theory to put gravitational lensing on a rigorous mathematical foundation.
Real and Complex Singularities by Laurentiu Paunescu Pdf
The modern theory of singularities provides a unifying theme that runs through fields of mathematics as diverse as homological algebra and Hamiltonian systems. It is also an important point of reference in the development of a large part of contemporary algebra, geometry and analysis. Presented by internationally recognized experts, the collection of articles in this volume yields a significant cross-section of these developments. The wide range of surveys includes an authoritative treatment of the deformation theory of isolated complex singularities by prize-winning researcher K Miyajima. Graduate students and even ambitious undergraduates in mathematics will find many research ideas in this volume and non-experts in mathematics can have an overview of some classic and fundamental results in singularity theory. The explanations are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to go further into the subject and explore the research literature.
Principles of Gravitational Lensing by Arthur B. Congdon,Charles R. Keeton Pdf
This textbook provides an introduction to gravitational lensing, which has become an invaluable tool in modern astrophysics, with applications that range from finding planets orbiting distant stars to understanding how dark matter and dark energy conspired to form the cosmic structures we see today. Principles of Gravitational Lensing begins with Einstein’s prediction that gravity bends light, and shows how that fundamental idea has spawned a rich field of study over the past century. The gravitational deflection of light was first detected by Eddington during a solar eclipse in May 1919, launching Einstein and his theory of relativity into public view. Yet the possibility of using the phenomenon to unlock mysteries of the Universe seemed remote, given the technology of the day. Theoretical work was carried out sporadically over the next six decades, but only with the discovery of the system Q0957+561 in 1979 was gravitational lensing transformed from a curiosity of general relativity into a practical observational tool. This book describes how the three subfields known as strong lensing, weak lensing, and microlensing have grown independently but become increasingly intertwined. Drawing on their research experience, Congdon and Keeton begin with the basic physics of light bending, then present the mathematical foundations of gravitational lensing, building up to current research topics in a clear and systematic way. Relevant background material from physics and mathematics is included, making the book self-contained. The derivations and explanations are supplemented by exercises designed to help students master the theoretical concepts as well as the methods that drive current research. An extensive bibliography guides those wishing to delve more deeply into particular areas of interest. Principles of Gravitational Lensing is ideal for advanced students and seasoned researchers looking to penetrate this thriving subject and even contribute research of their own.
Gravitational Lensing and Optical Geometry by Marcus C.Werner Pdf
The year 2019 saw the centenary of Eddington's eclipse expeditions and the corroboration of Einstein's general relativity by gravitational lensing. To mark the occasion, a Special Issue of Universe has been dedicated to the theoretical aspects of strong gravitational lensing. The articles assembled in this volume contain original research and reviews and apply a variety of mathematical techniques that have been developed to study this effect, both in 3-space and in spacetime. These include: · Mathematical properties of the standard thin lens approximation, in particular caustics; · Optical geometry, the Gauss–Bonnet method and related approaches; · Lensing in the spacetime of general relativity and modified theories; black hole shadows.
Gravitational Lensing and Microlensing by Silvia Mollerach,Esteban Roulet Pdf
This book provides a comprehensive and self-contained exposition of gravitational lensing phenomena. It presents the up-to-date status of gravitational lensing and microlensing, covering the cosmological applications of the observed lensing by galaxies, clusters and the large scale structures, as well as the microlensing searches in the Local Group and its applications to unveil the nature of the galactic dark matter, the search for planetary objects and the distribution of faint stars in our galaxy. Gravitational Lensing and Microlensing is pitched at the level of the graduate student interested in the issues of astrophysics and cosmology, and should be useful for specialist researchers as well. Contents:Historical IntroductionThe Deflection of LightGravitational Lensing TheoryMacrolensing ResultsMicrolensing I: BasicsMicrolensing II: Beyond the Simplest Light CurveCosmology Tools Readership: Graduate students, researchers and academics in astrophysics, astronomy and cosmology. Keywords:Gravitational Lensing;Microlensing;Deflection of Light;MacrolensingReviews:“… here one can find a complete overview of all the recent revolutionary developments of gravitational lensing, with a fully self-consistent treatment of microlensing. The quality and number of didactic illustrations is high … I think that this book should not be missing in scientific libraries that are to be updated on gravitational lensing. It also provides a useful support tool for basic gravitational lensing courses. Finally it can be recommended to researchers who want a rapid overview of the field, without getting swamped into too many details.”General Relativity and Gravitation
Introduction to Gravitational Lensing by Massimo Meneghetti Pdf
This book introduces the phenomenology of gravitational lensing in an accessible manner and provides a thorough discussion of the related astrophysical applications. It is intended for advanced undergraduates and graduate students who want to start working in this rapidly evolving field. This includes also senior researchers who are interested in ongoing or future surveys and missions such as DES, Euclid, WFIRST, LSST. The reader is guided through many fascinating topics related to gravitational lensing like the structure of our galaxy, the searching for exoplanets, the investigation of dark matter in galaxies and galaxy clusters, and several aspects of cosmology, including dark energy and the cosmic microwave background. The author, who has gained valuable experience as academic teacher, guides the readers towards the comprehension of the theory of gravitational lensing and related observational techniques by using simple codes written in python. This approach, beyond facilitating the understanding of gravitational lensing, is preparatory for learning the python programming language which is gaining large popularity both in academia and in the private sector.
Gravitational Lensing: Strong, Weak and Micro by Peter Schneider,Christopher Kochanek,Joachim Wambsganss Pdf
The observation, in 1919 by A.S. Eddington and collaborators, of the gra- tational de?ection of light by the Sun proved one of the many predictions of Einstein’s Theory of General Relativity: The Sun was the ?rst example of a gravitational lens. In 1936, Albert Einstein published an article in which he suggested - ing stars as gravitational lenses. A year later, Fritz Zwicky pointed out that galaxies would act as lenses much more likely than stars, and also gave a list of possible applications, as a means to determine the dark matter content of galaxies and clusters of galaxies. It was only in 1979 that the ?rst example of an extragalactic gravitational lens was provided by the observation of the distant quasar QSO 0957+0561, by D. Walsh, R.F. Carswell, and R.J. Weymann. A few years later, the ?rst lens showing images in the form of arcs was detected. The theory, observations, and applications of gravitational lensing cons- tute one of the most rapidly growing branches of astrophysics. The gravi- tional de?ection of light generated by mass concentrations along a light path producesmagni?cation,multiplicity,anddistortionofimages,anddelaysp- ton propagation from one line of sight relative to another. The huge amount of scienti?c work produced over the last decade on gravitational lensing has clearly revealed its already substantial and wide impact, and its potential for future astrophysical applications.
The Relativistic Boltzmann Equation: Theory and Applications by Carlo Cercignani,Gilberto M. Kremer Pdf
The aim of this book is to present the theory and applications of the relativistic Boltzmann equation in a self-contained manner, even for those readers who have no familiarity with special and general relativity. Though an attempt is made to present the basic concepts in a complete fashion, the style of presentation is chosen to be appealing to readers who want to understand how kinetic theory is used for explicit calculations. The book will be helpful not only as a textbook for an advanced course on relativistic kinetic theory but also as a reference for physicists, astrophysicists and applied mathematicians who are interested in the theory and applications of the relativistic Boltzmann equation.
Einstein’s Field Equations and Their Physical Implications by Bernd G. Schmidt Pdf
This book serves two purposes. The authors present important aspects of modern research on the mathematical structure of Einstein's field equations and they show how to extract their physical content from them by mathematically exact methods. The essays are devoted to exact solutions and to the Cauchy problem of the field equations as well as to post-Newtonian approximations that have direct physical implications. Further topics concern quantum gravity and optics in gravitational fields. The book addresses researchers in relativity and differential geometry but can also be used as additional reading material for graduate students.
Analysis and Mathematical Physics by Björn Gustafsson,Alexander Vasil'ev Pdf
Our knowledge of objects of complex and potential analysis has been enhanced recently by ideas and constructions of theoretical and mathematical physics, such as quantum field theory, nonlinear hydrodynamics, material science. These are some of the themes of this refereed collection of papers, which grew out of the first conference of the European Science Foundation Networking Programme 'Harmonic and Complex Analysis and Applications' held in Norway 2007.
Accompanying CD-ROM contains Microsoft Windows program Kepler which calculates the effects of any perturbation of the Kepler problem and plots the resulting trajectories.
Primordial Cosmology by Patrick Peter,Jean-Philippe Uzan Pdf
This book provides an extensive survey of all the physics necessary to understand the current developments in the field of fundamental cosmology, as well as an overview of the observational data and methods. It will help students to get into research by providing definitions and main techniques and ideas discussed today. The book is divided into three parts. Part 1 summarises the fundamentals in theoretical physics needed in cosmology (general relativity, field theory, particle physics). Part 2 describes the standard model of cosmology and includes cosmological solutions of Einstein equations, the hot big bang model, cosmological perturbation theory, cosmic microwave background anisotropies, lensing and evidence for dark matter, and inflation. Part 3 describes extensions of this model and opens up current research in the field: scalar-tensor theories, supersymmetry, the cosmological constant problem and acceleration of the universe, topology of the universe, grand unification and baryogenesis, topological defects and phase transitions, string inspired cosmology including branes and the latest developments. The book provides details of all derivations and leads the student up to the level of research articles.
The Singularity School and Conference took place in Luminy, Marseille, from January 24th to February 25th 2005. More than 180 mathematicians from over 30 countries converged to discuss recent developments in singularity theory.The volume contains the elementary and advanced courses conducted by singularities specialists during the conference, general lectures on singularity theory, and lectures on applications of the theory to various domains. The subjects range from geometry and topology of singularities, through real and complex singularities, to applications of singularities.
Natural Focusing and Fine Structure of Light by J.F Nye Pdf
A new kind of optics has grown up during the last 25 years. Geometrical optics has been studied for centuries (the law of reflection was known to the ancient Greeks) and wave optics (heralded by Huygens' Treatise on Light) has been studied for more than 300 years. But in the mid 1970s it began to be understood that when natural processes focus light, as when sunlight is reflected from the sea at sunset, the light caustics that are produced have a systematic behavior previously unrecognized. Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations provides a definitive account of how classical optics has been reconstructed in a modern way by emphasizing the hierarchy of singularities that exists in light fields. The book discusses the singularities of geometrical optics and their systematization by catastrophe theory. It explores the diffraction patterns associated with caustics that are dominated by wave dislocations, line singularities of the phase, and analogous to crystal dislocations. The book is a perfect blend of mathematics and physics, combining theory, computer simulation, and beautiful experimental photographs of the phenomena studied.