Deterministic Chaos in General Relativity PDF Download
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Author: David Hobill
Publisher: Springer Science & Business Media
ISBN: 1475799934
Category : Science
Languages : en
Pages : 472
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Book Description
Nonlinear dynamical systems play an important role in a number of disciplines. The physical, biological, economic and even sociological worlds are comprised of com plex nonlinear systems that cannot be broken down into the behavior of their con stituents and then reassembled to form the whole. The lack of a superposition principle in such systems has challenged researchers to use a variety of analytic and numerical methods in attempts to understand the interesting nonlinear interactions that occur in the World around us. General relativity is a nonlinear dynamical theory par excellence. Only recently has the nonlinear evolution of the gravitational field described by the theory been tackled through the use of methods used in other disciplines to study the importance of time dependent nonlinearities. The complexity of the equations of general relativity has been (and still remains) a major hurdle in the formulation of concrete mathematical concepts. In the past the imposition of a high degree of symmetry has allowed the construction of exact solutions to the Einstein equations. However, most of those solutions are nonphysical and of those that do have a physical significance, many are often highly idealized or time independent.
Author: David Hobill
Publisher: Springer Science & Business Media
ISBN: 1475799934
Category : Science
Languages : en
Pages : 472
Get Book Here
Book Description
Nonlinear dynamical systems play an important role in a number of disciplines. The physical, biological, economic and even sociological worlds are comprised of com plex nonlinear systems that cannot be broken down into the behavior of their con stituents and then reassembled to form the whole. The lack of a superposition principle in such systems has challenged researchers to use a variety of analytic and numerical methods in attempts to understand the interesting nonlinear interactions that occur in the World around us. General relativity is a nonlinear dynamical theory par excellence. Only recently has the nonlinear evolution of the gravitational field described by the theory been tackled through the use of methods used in other disciplines to study the importance of time dependent nonlinearities. The complexity of the equations of general relativity has been (and still remains) a major hurdle in the formulation of concrete mathematical concepts. In the past the imposition of a high degree of symmetry has allowed the construction of exact solutions to the Einstein equations. However, most of those solutions are nonphysical and of those that do have a physical significance, many are often highly idealized or time independent.
Author: Vladimir Belinski
Publisher: Cambridge University Press
ISBN: 1107047471
Category : Science
Languages : en
Pages : 279
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Book Description
This book mathematically derives the theory underlying the Belinski-Khalatnikov-Lifshitz conjecture on the general solution of the Einstein equations with a cosmological singularity.
Author: Santo Banerjee
Publisher: Springer
ISBN: 9401786917
Category : Science
Languages : en
Pages : 201
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Book Description
The present work investigates global politics and political implications of social science and management with the aid of the latest complexity and chaos theories. Until now, deterministic chaos and nonlinear analysis have not been a focal point in this area of research. This book remedies this deficiency by utilizing these methods in the analysis of the subject matter. The authors provide the reader a detailed analysis on politics and its associated applications with the help of chaos theory, in a single edited volume.
Author: Bernd G. Schmidt
Publisher: Springer
ISBN: 3540465804
Category : Mathematics
Languages : en
Pages : 443
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Book Description
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.
Author: Carlos Martins
Publisher: Springer Science & Business Media
ISBN: 9401732728
Category : Science
Languages : en
Pages : 257
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Book Description
The workshop on The Cosmology of Extra Dimensions and Varying Fundamental Constants, which was part of JENAM 2002, was held at the Physics Department of the University of Porto (FCUP) from the 3rd to the 5th of September 2002. It was regularly attended by about 110 participants, of which 65 were officially registered in the VFC workshop, while the others came from the rest of the JENAM workshops. There were also a few science correspondents from the national and international press. During the 3 days of the scientific programme, 8 Invited Reviews and 30 Oral Communications were presented. The speakers came from 11 different European countries, and also from Argentina, Australia, Canada, Japan and the U.S.A. There were also speakers from six Portuguese research institutions, and nine of the speak ers were Ph.D. students. The contributions are presented in these proceedings in chronological order. The workshop brought together string theorists, particle physicists, theoretical and observational cosmologists, relativists and observational astrophysicists. It was generally agreed that this inter-disciplinarity was the greatest strength of the work shop, since it provided people coming into this very recent topic from the various different backgrounds with an opportunity to understand each other's language and thereby gain a more solid understanding of the overall picture.
Author: Petr Hájek
Publisher: Cambridge University Press
ISBN: 1107168023
Category : Mathematics
Languages : en
Pages : 331
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Book Description
The proceedings of the conference 'Logical Foundations of Mathematics, Computer Science, and Physics - Kurt Gödel's Legacy', held in Brno, Czech Republic, on the 90th anniversary of Gödel's birth. The papers in this volume cover the wide range of topics Gödel's work touched, and affirm its continuing importance.
Author: Abhay Ashtekar
Publisher: Springer
ISBN: 3642419925
Category : Science
Languages : en
Pages : 883
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Book Description
The Springer Handbook of Spacetime is dedicated to the ground-breaking paradigm shifts embodied in the two relativity theories, and describes in detail the profound reshaping of physical sciences they ushered in. It includes in a single volume chapters on foundations, on the underlying mathematics, on physical and astrophysical implications, experimental evidence and cosmological predictions, as well as chapters on efforts to unify general relativity and quantum physics. The Handbook can be used as a desk reference by researchers in a wide variety of fields, not only by specialists in relativity but also by researchers in related areas that either grew out of, or are deeply influenced by, the two relativity theories: cosmology, astronomy and astrophysics, high energy physics, quantum field theory, mathematics, and philosophy of science. It should also serve as a valuable resource for graduate students and young researchers entering these areas, and for instructors who teach courses on these subjects. The Handbook is divided into six parts. Part A: Introduction to Spacetime Structure. Part B: Foundational Issues. Part C: Spacetime Structure and Mathematics. Part D: Confronting Relativity theories with observations. Part E: General relativity and the universe. Part F: Spacetime beyond Einstein.
Author: John Earman
Publisher: Oxford University Press
ISBN: 0195344642
Category : Science
Languages : en
Pages : 270
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Book Description
Almost from its inception, Einstein's general theory of relativity was known to sanction spacetime models harboring singularities. Until the 1960s, however, spacetime singularities were thought to be artifacts of the idealizations of the models. This attitude evaporated in the face of a series of theorems, due largely to Stephen Hawking and Roger Penrose, which showed that Einstein's general theory implies that singularities can be expected to occur in a wide variety of conditions in both gravitational collapse and in cosmology. In the light of these results some physicists adopted the attitude that, since spacetime singularities are intolerable, general relativity contains within itself the seeds of its own destruction. Others hoped that peaceful coexistence with singularities could be achieved by proving a form of Roger Penrose's cosmic censorship hypothesis, which would place singularities safely inside black holes. Whatever the attitude one adopts toward spacetime singularities, it is evident that they raise a number of foundational problems for physics and have profound implications for the philosophy of space and time. However, philosophers of science have been slow to awaken to the significance of these developments. Indeed, this is the first serious book-length study of the subject by a philosopher of science. It features an overview of the literature on singularities, as well as an analytic commentary on their significance to a number of scientific and philosophical issues.
Author: Héctor J. De Vega
Publisher: Springer Science & Business Media
ISBN: 940100997X
Category : Science
Languages : en
Pages : 589
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Book Description
A fundamental, profound review of the key issues relating to the early universe and the physical processes that occurred in it. The interplay between cosmic microwave background radiation, large scale structure, and the dark matter problem are stressed, with a central focus on the crucial issue of the phase transitions in the early universe and their observable consequences: baryon symmetry, baryogenesis and cosmological fluctuations. There is an interplay between cosmology, statistical physics and particle physics in studying these problems, both at the theoretical and the experimental / observational levels. Special contributions are devoted to primordial and astrophysical black holes and to high energy cosmic rays and neutrino astrophysics. There is also a special section devoted to the International Space Station and its scientific utilization.
Author: George F. R. Ellis
Publisher: Cambridge University Press
ISBN: 0521381150
Category : Science
Languages : en
Pages : 637
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Book Description
Surveying key developments and open issues in cosmology for graduate students and researchers, this book focuses on the general concepts and relations that underpin the standard model of the Universe. It also examines anisotropic and inhomogeneous models, and deeper issues, such as quantum cosmology and the multiverse proposal.
