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A comprehensive review of the testing and research conducted on Einstein's theory of general relativity.
Gravity and Gravitation is a physics book that is written in a form that is easy to understand for high school and beginning college students, as well as science buffs. It is based on the lessons from the School for Champions educational website.The book explains the principles of gravity and gravitation, shows derivations of important gravity equations, and provides applications of those equations. It also compares the different theories of gravitation, from those of Newton to Einstein to present-day concepts.
Spacetime physics -- Physics in flat spacetime -- The mathematics of curved spacetime -- Einstein's geometric theory of gravity -- Relativistic stars -- The universe -- Gravitational collapse and black holes -- Gravitational waves -- Experimental tests of general relativity -- Frontiers
This is an introductory book on the general theory of relativity based partly on lectures given to students of M.Sc. Physics at my university. The book is divided into three parts. The ?rst part is a preliminary course on general relativity with minimum preparation. The second part builds the ma- ematical background and the third part deals with topics where mathematics developed in the second part is needed. The ?rst chapter gives a general background and introduction. This is f- lowed by an introduction to curvature through Gauss’ Theorema Egregium. This theorem expresses the curvature of a two-dimensional surface in terms of intrinsic quantitiesrelatedtothein?nitesimaldistancefunctiononthesurface.Thestudent isintroducedtothemetrictensor,Christo?elsymbolsandRiemanncurvaturet- sor by elementary methods in the familiar and visualizable case of two dimensions. This early introduction to geometric quantities equips a student to learn simpler topics in general relativity like the Newtonian limit, red shift, the Schwarzschild solution, precession of the perihelion and bending of light in a gravitational ?eld. Part II (chapters 5 to 10) is an introduction to Riemannian geometry as - quired by general relativity. This is done from the beginning, starting with vectors and tensors. I believe that students of physics grasp physical concepts better if they are not shaky about the mathematics involved.
One of the most challenging problems of contemporary theoretical physics is the mathematically rigorous construction of a theory which describes gravitation and the other fundamental physical interactions within a common framework. The physical ideas which grew from attempts to develop such a theory require highly advanced mathematical methods and radically new physical concepts. This book presents different approaches to a rigorous unified description of quantum fields and gravity. It contains a carefully selected cross-section of lively discussions which took place in autumn 2010 at the fifth conference "Quantum field theory and gravity - Conceptual and mathematical advances in the search for a unified framework" in Regensburg, Germany. In the tradition of the other proceedings covering this series of conferences, a special feature of this book is the exposition of a wide variety of approaches, with the intention to facilitate a comparison. The book is mainly addressed to mathematicians and physicists who are interested in fundamental questions of mathematical physics. It allows the reader to obtain a broad and up-to-date overview of a fascinating active research area.
The revised and updated 2nd edition of this established textbook provides a self-contained introduction to the general theory of relativity, describing not only the physical principles and applications of the theory, but also the mathematics needed, in particular the calculus of differential forms. Updated throughout, the book contains more detailed explanations and extended discussions of several conceptual points, and strengthened mathematical deductions where required. It includes examples of work conducted in the ten years since the first edition of the book was published, for example the pedagogically helpful concept of a "river of space" and a more detailed discussion of how far the principle of relativity is contained in the general theory of relativity. Also presented is a discussion of the concept of the 'gravitational field' in Einstein's theory, and some new material concerning the 'twin paradox' in the theory of relativity. Finally, the book contains a new section about gravitational waves, exploring the dramatic progress in this field following the LIGO observations. Based on a long-established masters course, the book serves advanced undergraduate and graduate level students, and also provides a useful reference for researchers.
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.
“Newton’s Gravity” conveys the power of simple mathematics to tell the fundamental truth about nature. Many people, for example, know the tides are caused by the pull of the Moon and to a lesser extent the Sun. But very few can explain exactly how and why that happens. Fewer still can calculate the actual pulls of the Moon and Sun on the oceans. This book shows in clear detail how to do this with simple tools. It uniquely crosses disciplines – history, astronomy, physics and mathematics – and takes pains to explain things frequently passed over or taken for granted in other books. Using a problem-based approach, “Newton’s Gravity” explores the surprisingly basic mathematics behind gravity, the most fundamental force that governs the movements of satellites, planets, and the stars. Author Douglas W. MacDougal uses actual problems from the history of astronomy, as well as original examples, to deepen understanding of how discoveries were made and what they mean. “Newton’s Gravity” concentrates strongly on the development of the science of orbital motion, beginning with Galileo, Kepler, and Newton, each of whom is prominently represented. Quotes and problems from Galileo’s Dialogs Concerning Two New Sciences and particularly Newton’s Principia help the reader get inside the mind of those thinkers and see the problems as they saw them, and experience their concise and typically eloquent writing. This book enables students and curious minds to explore the mysteries of celestial motion without having to know advanced mathematics. It will whet the reader’s curiosity to explore further and provide him or her the tools (mathematical or physical) to do so.
Here it is, in a nutshell: the history of one genius’s most crucial work – discoveries that were to change the face of modern physics. In the early 1900s, Albert Einstein formulated two theories that would forever change the landscape of physics: the Special Theory of Relativity and the General Theory of Relativity. Respected American academic Professor Tai Chow tells us the story of these discoveries. He details the basic ideas of Einstein, including his law of gravitation. Deftly employing his inimitable writing style, he goes on to explain the physics behind black holes, weaving into his account an explanation of the structure of the universe and the science of cosmology.
Beyond Einstein: Perspectives on Geometry, Gravitation, and Cosmology explores the rich interplay between mathematical and physical ideas by studying the interactions of major actors and the roles of important research communities over the course of the last century.