Download or read book Gravitational Lensing and Optical Geometry written by Marcus C.Werner and published by MDPI. This book was released on 2020-12-08 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Gravitational Lensing and Optical Geometry written by Marcus C. Werner and published by . This book was released on 2020 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Ray Optics Fermat s Principle and Applications to General Relativity written by Volker Perlick and published by Springer Science & Business Media. This book was released on 2003-07-01 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the mathematical theory of light propagation in media on general-relativistic spacetimes. The first part discusses the transition from Maxwell's equations to ray optics. The second part establishes a general mathematical framework for treating ray optics as a theory in its own right, making extensive use of the Hamiltonian formalism. This part also includes a detailed discussion of variational principles (i.e., various versions of Fermat's principle) for light rays in general-relativistic media. Some applications, e.g. to gravitational lensing, are worked out. The reader is assumed to have some basic knowledge of general relativity and some familiarity with differential geometry. Some of the results are published here for the first time, e.g. a general-relativistic version of Fermat's principle for light rays in a medium that has to satisfy some regularity condition only.
Download or read book Introduction To Geometrical Optics written by Milton Katz and published by World Scientific Publishing Company. This book was released on 2002-12-10 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the culmination of twenty-five years of teaching Geometrical Optics. The volume is organised such that the single spherical refracting surface is the basic optical element. Spherical mirrors are treated as special cases of refraction, with the same applicable equations. Thin lens equations follow as combinations of spherical refracting surfaces while the cardinal points of the thick lens make it equivalent to a thin lens. Ultimately, one set of vergence equations are applicable to all these elements.The chapters are devoted to in-depth treatments of stops, pupils and ports; magnifiers, microscopes, telescopes, and camera lenses; ophthalmic instruments; resolving power and MTF; trigonometric ray tracing; and chromatic and monochromatic aberrations. There are over 100 worked examples, 400 homework problems and 400 illustrations.First published in 1994 by Penumbra Publishing Co.
Download or read book Einstein s Telescope The Hunt for Dark Matter and Dark Energy in the Universe written by Evalyn Gates and published by W. W. Norton & Company. This book was released on 2010-02-22 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: "In Einstein’s Telescope, Evalyn Gates, an expert on all that’s dark in the universe, brings dark matter, dark energy, and even black holes to light." —Neil deGrasse Tyson, astrophysicist, American Museum of Natural History, and New York Times best-selling author of Astrophysics for People in a Hurry In 1936, Albert Einstein predicted that gravitational distortions would allow space itself to act as a telescope far more powerful than humans could ever build. Now, cosmologists at the forefront of their field are using this radical technique ("Einstein’s Telescope") to detect the invisible. In fresh, engaging prose, astrophysicist Evalyn Gates explains how this tool is enabling scientists to uncover planets as big as the Earth, discover black holes as they whirl through space, and trace the evolution of cosmic architecture over billions of years. Powerful and accessible, Einstein’s Telescope takes us to the brink of a revolution in our understanding of the deepest mysteries of the Universe.
Download or read book Introduction to Gravitational Lensing written by Massimo Meneghetti and published by Springer Nature. This book was released on 2021-12-10 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Galileo Unbound written by David D. Nolte and published by Oxford University Press. This book was released on 2018-07-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.
Download or read book A Treatise on Geometrical Optics written by Robert Alfred Herman and published by . This book was released on 1900 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Ray and Wave Theory of Lenses written by A. Walther and published by Cambridge University Press. This book was released on 2006-11-02 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a detailed description of lens behaviour in real optical systems.
Download or read book Gravitational Lenses written by Rainer Kayser and published by Springer. This book was released on 1992 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most spectacular predictions of Einstein's theory of general relativity is the occurrence of gravitational lenses in our galactic system. Nowadays the mastering of the mathematics together with the technology available to astronomers allow Einstein's prediction to be confirmed. Several reviews here give the reader the chance to under- stand the basic theoretical concept of gravitational lensing and to obtain an overview of observational work. The present state of the field and latest results are given in a large number of specialized papers. Anextensive source and subject index make these proceedings valuable also as areference book for all researchers active in the field.
Download or read book The Extragalactic Distance Scale written by Space Telescope Science Institute (U.S.). Symposium and published by Cambridge University Press. This book was released on 1997-06-28 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the hottest debates in astronomy and cosmology today concerns the value of the Hubble constant. This constant is of paramount importance since it fixes the size and age of the Universe. At a symposium at the Space Telescope Science Institute, experts from around the world presented the latest results from a plethora of techniques for determining the Hubble constant. The value has always been controversial, but at this meeting experts' results agreed for the first time to within about 20%. Based on the meeting, this book presents twenty-three specially written review articles. They provide a comprehensive account of the Hubble-constant debate with the latest results from gravitational lensing, supernovae and novae, the Tully-Fisher relation, the Sunyaev-Zeldovich effect, globular clusters, planetary nebulae, light echoes, and the Hubble Space Telescope Key Project. This timely volume provides a standard reference for graduate students and researchers in astronomy and cosmology.
Download or read book Gravitational Lensing Strong Weak and Micro written by Peter Schneider and published by Springer Science & Business Media. This book was released on 2006-12-30 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Dark Matter and Gravitational Lensing as Teaching Tools for Physics and Astronomy written by Silvia Simionato and published by . This book was released on 2022* with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work, mainly aimed at teachers of physics, mathematics and astronomy, it is illustrated how two important topics of cosmology can be introduced as valuable teaching aids: the dark matter problem and gravitational lensing. These complex and articulated topics have been treated with appropriate elementarisation and the use of simplified models, that made them suitable for introduction into the classroom in the form of exercises and/or extracurricular projects for students in their final years of secondary school or first years of university. In the first part of this thesis, the concepts of radial and rotational velocity, together with those of spider diagram and rotation curve, are introduced and applied to the solar system and a spiral galaxy. The inclusion of the spider diagram in this educational context is innovative. All this is discussed while working with real data and using the dynamic mathematical software Geogebra. Finally, we estimate the amount of non-visible mass that apparently influences the motion of all matter in a spiral galaxy. This provides evidence for the possible existence of dark matter. In the second part, we discuss the phenomenon of strong gravitational lensing, which can produce optical illusions observable in the universe. This effect is investigated for several examples of mass distributions acting as lenses. By examining the geometry of the gravitational lens system, we deduce size, distances and alignment of the components. Using this information and thanks to the software Geogebra, visualisations and interactive simulations of the images resulting from the gravitational lensing effect are created. Finally, the form to be given to lenses made of glass, to recreate the same effects produced by gravitational lenses, is studied. We have designed and produced five models of plexiglass lenses, that add an experimental part to the teaching of this subject, as they reproduce the gravitational lens effect directly in the classroom.
Download or read book Geometrical Optics written by W. T. Welford and published by . This book was released on 1962 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mirrors Prisms and Lenses written by James Powell Cocke Southall and published by . This book was released on 1964 with total page 874 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Riemann Finsler Geometry written by D. Bao and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the elementary but essential problems in Riemann-Finsler Geometry, which include a repertoire of rigidity and comparison theorems, and an array of explicit examples, illustrating many phenomena which admit only Finslerian interpretations. "This book offers the most modern treatment of the topic ..." EMS Newsletter.
Download or read book Spacetime and Geometry written by Sean M. Carroll and published by Cambridge University Press. This book was released on 2019-08-08 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introductory textbook on general relativity, covering the theory's foundations, mathematical formalism and major applications.
