Deterministic Chaos in General Relativity

By: D. Hobill, NATO Advanced Research Workshop on Deter, David Hobill (Editor)

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Hardcover | 30 September 1994

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492 Pages

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26.04 x 17.15 x 3.18

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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.

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You Can Find This Book In

Non-Fiction Science Physics Relativity Physics Mathematics Applied Mathematics Chaos Theory Engineering & Technology Technology in General Maths for Engineers Science in General Maths for Scientists

Mathematical Physics

A Brief Review of "Deterministic Chaos in General Relativity"	p. 1
Introduction to Dynamical Systems	p. 19
A Short Course on Chaotic Hamiltonian Systems	p. 63
Geometry of Perturbation Theory	p. 89
Between Integrability and Chaos	p. 103
On Defining Chaos in the Absence of Time	p. 107
On the Dynamics of Generators of Cauchy Horizons	p. 113
Chaos in the Case of Two Fixed Black Holes	p. 129
Particle Motion Around Perturbed Black Holes: The Onset of Chaos	p. 145
Critical Behaviour in Scalar Field Collapse	p. 155
Relativistic Cosmologies	p. 179
Homoclinic Chaos in Relativistic Cosmology	p. 203
Mixing Properties of [kappa] = -1 FLRW Models	p. 237
Classical and Quantum Chaos in Robertson-Walker Cosmologies	p. 251
Relativistic Fractal Cosmologies	p. 269
Self-Similar Asymptotic Solutions of Einstein's Equations	p. 297
Nonlinearly Interacting Gravitational Waves in the Gowdy T[superscript 3] Cosmology	p. 307
The Mixmaster Cosmological Metrics	p. 317
The Belinskii-Khalatnikov-Lifshitz Discrete Evolution as an Approximation to Mixmaster Dynamics	p. 329
How Can You Tell if the Bianchi IX Models Are Chaotic?	p. 345
The Chaoticity of the Bianchi IX Cosmological Model	p. 355
Chaos in the Einstein Equations-Characterization and Importance?	p. 359
Integrability of the Mixmaster Universe	p. 423
Continuous Time Dynamics and Iterative Maps of Ellis-MacCallum-Wainwright Variables	p. 433
A Dynamical Systems Approach to the Oscillatory Singularity in Bianchi Cosmologies	p. 449
Participants	p. 463
Index	p. 467
Table of Contents provided by Blackwell. All Rights Reserved.

Deterministic Chaos in General Relativity

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