Equations of Motion in Relativistic Gravity

Fundamental Theories of Physics

Free sample

The present volume aims to be a comprehensive survey on the derivation of the equations of motion, both in General Relativity as well as in alternative gravity theories. The topics covered range from the description of test bodies, to self-gravitating (heavy) bodies, to current and future observations.

Emphasis is put on the coverage of various approximation methods (e.g., multipolar, post-Newtonian, self-force methods) which are extensively used in the context of the relativistic problem of motion. Applications discussed in this volume range from the motion of binary systems -- and the gravitational waves emitted by such systems -- to observations of the galactic center. In particular the impact of choices at a fundamental theoretical level on the interpretation of experiments is highlighted.

This book provides a broad and up-do-date status report, which will not only be of value for the experts working in this field, but also may serve as a guideline for students with background in General Relativity who like to enter this field.
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About the author

Bernard Schutz has done research and teaching in general relativity and especially its applications in astronomy since 1970. He is the author of more than 200 publications, including Geometrical Methods of Mathematical Physics and Gravity from the Ground Up (both published by Cambridge University Press). Schutz currently specialises in gravitational wave research, studying the theory of potential sources and designing new methods for analysing the data from current and planned detectors. He is a member of most of the current large-scale gravitational wave projects: GEO600 (of which he is a PI), the LIGO Scientific Collaboration, and LISA. Schutz is a Director of the Max Planck Institute for Gravitational Physics, also known as the Albert Einstein Institute (AEI), in Potsdam, Germany. He holds a part-time chair in Physics and Astronomy at Cardiff University, Wales, as well as honorary professorships at Potsdam and Hanover universities in Germany. Educated in the USA, he taught physics and astronomy for twenty years at Cardiff before moving to Germany in 1995 to the newly-founded AEI. In 1998 he founded the open-access online journal Living Reviews in Relativity. The Living Reviews family now includes six journals. In 2006 he was awarded the Amaldi Gold Medal of the Italian Society for Gravitation (SIGRAV), and in 2011 he received an honorary DSc from the University of Glasgow. He is a Fellow of the American Physical Society and the Institute of Physics, an Honorary Fellow of the Royal Astronomical Society, and a member of the Learned Society of Wales, the German Academy of Natural Sciences Leopoldina and the Royal Society of Arts and Sciences, Uppsala.

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Additional Information

Publisher
Springer
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Published on
Jun 1, 2015
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Pages
840
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ISBN
9783319183350
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Language
English
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Genres
Mathematics / Applied
Science / Gravity
Science / Physics / General
Science / Physics / Mathematical & Computational
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Content Protection
This content is DRM protected.
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This book describes a relativistic quantum theory developed by the author starting from the E.C.G. Stueckelberg approach proposed in the early 40s. In this framework a universal invariant evolution parameter (corresponding to the time originally postulated by Newton) is introduced to describe dynamical evolution. This theory is able to provide solutions for some of the fundamental problems encountered in early attempts to construct a relativistic quantum theory. A relativistically covariant construction is given for which particle spins and angular momenta can be combined through the usual rotation group Clebsch-Gordan coefficients. Solutions are defined for both the classical and quantum two body bound state and scattering problems. The recently developed quantum Lax-Phillips theory of semi group evolution of resonant states is described. The experiment of Lindner and coworkers on interference in time is discussed showing how the property of coherence in time provides a simple understanding of the results. The full gauge invariance of the Stueckelberg-Schroedinger equation results in a 5D generalization of the usual gauge theories. A description of this structure and some of its consequences for both Abelian and non-Abelian fields are discussed. A review of the basic foundations of relativistic classical and quantum statistical mechanics is also given. The Bekenstein-Sanders construction for imbedding Milgrom's theory of modified spacetime structure into general relativity as an alternative to dark matter is also studied.
This primer offers a concise introduction to Loop Quantum Gravity (LQG)
- a theoretical framework for uniting Quantum Mechanics (QM) with General Relativity (GR). The emphasis is on the physical aspects of the framework and its historical development in terms of self-dual variables, still most suited for a first, pedagogical encounter with LQG.

The text starts by reviewing GR and the very basics of Quantum Field Theory (QFT), and then explains in a concise and clear manner the steps leading from the Einstein-Hilbert action for gravity to the construction of the quantum states of geometry, known as spin-networks, and which provide the basis for the kinematical Hilbert space of quantum general relativity. Along the way the various associated concepts of tetrads, spin-connection and holonomies are introduced.

Having thus provided a minimal introduction to the LQG framework, some applications to the problems of black hole entropy and of quantum cosmology are briefly surveyed. Last but not least, a list of the most common criticisms of LQG is presented, which are then tackled one by one in order to convince the reader of the physical viability of the theory. A set of appendices provides accessible introductions to several key notions such as the Peter-Weyl theorem, duality of differential forms and Regge calculus, among others.

The presentation is aimed at graduate students and researchers who have some familiarity with the tools of QM and GR, but are intimidated by the technicalities required to browse through the existing LQG literature. This primer aims at making the formalism appear a little less bewildering to the uninitiated and helps lower the barrier for entry into the field.
This is a book about physics, written for mathematicians. The readers we have in mind can be roughly described as those who: I. are mathematics graduate students with some knowledge of global differential geometry 2. have had the equivalent of freshman physics, and find popular accounts of astrophysics and cosmology interesting 3. appreciate mathematical elarity, but are willing to accept physical motiva tions for the mathematics in place of mathematical ones 4. are willing to spend time and effort mastering certain technical details, such as those in Section 1. 1. Each book disappoints so me readers. This one will disappoint: 1. physicists who want to use this book as a first course on differential geometry 2. mathematicians who think Lorentzian manifolds are wholly similar to Riemannian ones, or that, given a sufficiently good mathematical back ground, the essentials of a subject !ike cosmology can be learned without so me hard work on boring detaiis 3. those who believe vague philosophical arguments have more than historical and heuristic significance, that general relativity should somehow be "proved," or that axiomatization of this subject is useful 4. those who want an encyclopedic treatment (the books by Hawking-Ellis [1], Penrose [1], Weinberg [1], and Misner-Thorne-Wheeler [I] go further into the subject than we do; see also the survey article, Sachs-Wu [1]). 5. mathematicians who want to learn quantum physics or unified fieId theory (unfortunateIy, quantum physics texts all seem either to be for physicists, or merely concerned with formaI mathematics).
This book describes a relativistic quantum theory developed by the author starting from the E.C.G. Stueckelberg approach proposed in the early 40s. In this framework a universal invariant evolution parameter (corresponding to the time originally postulated by Newton) is introduced to describe dynamical evolution. This theory is able to provide solutions for some of the fundamental problems encountered in early attempts to construct a relativistic quantum theory. A relativistically covariant construction is given for which particle spins and angular momenta can be combined through the usual rotation group Clebsch-Gordan coefficients. Solutions are defined for both the classical and quantum two body bound state and scattering problems. The recently developed quantum Lax-Phillips theory of semi group evolution of resonant states is described. The experiment of Lindner and coworkers on interference in time is discussed showing how the property of coherence in time provides a simple understanding of the results. The full gauge invariance of the Stueckelberg-Schroedinger equation results in a 5D generalization of the usual gauge theories. A description of this structure and some of its consequences for both Abelian and non-Abelian fields are discussed. A review of the basic foundations of relativistic classical and quantum statistical mechanics is also given. The Bekenstein-Sanders construction for imbedding Milgrom's theory of modified spacetime structure into general relativity as an alternative to dark matter is also studied.
There exist essentially two levels of investigation in theoretical physics. One is primarily descriptive, concentrating as it does on useful phenomenological approaches toward the most economical classifications of large classes of experimental data on particular phenomena. The other, whose thrust is explanatory, has as its aim the formulation of those underlying hypotheses and their mathematical representations that are capable of furnishing, via deductive analysis, predictions - constituting the particulars of universals (the asserted laws)- about the phenomena under consideration. The two principal disciplines of contemporary theoretical physics - quantum theory and the theory of relativity - fall basically into these respective categories. General Relativity and Matter represents a bold attempt by its author to formulate, in as transparent and complete a way as possible, a fundamental theory of matter rooted in the theory of relativity - where the latter is viewed as providing an explanatory level of understanding for probing the fundamental nature ofmatter indomainsranging all the way fromfermis and lessto light years and more. We hasten to add that this assertion is not meant to imply that the author pretends with his theory to encompass all ofphysics or even a tiny part of the complete objective understanding of our accessible universe. But he does adopt the philosophy that underlying all natural phenomena there is a common conceptualbasis,and then proceeds to investigate how far such a unified viewcan take us at its present stage of development.
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