The article reviews the current status of a theoretical approach to the problem of the emission of gravitational waves by isolated systems in the context of general relativity. Part A of the article deals with general post-Newtonian sources. The exterior field of the source is investigated by means of a combination of analytic post-Minkowskian and multipolar approximations. The physical observables in the far-zone of the source are described by a specific set of radiative multipole moments. By matching the exterior solution to the metric of the postNewtonian source in the near-zone we obtain the explicit expressions of the source multipole moments. The relationships between the radiative and source moments involve many nonlinear multipole interactions, among them those associated with the tails (and tails-of-tails) of gravitational waves. Part B of the article is devoted to the application to compact binary systems. We present the equations of binary motion, and the associated Lagrangian and Hamiltonian, at the third post-Newtonian (3PN) order beyond the Newtonian acceleration. The gravitational-wave energy flux, taking consistently into account the relativistic corrections in the binary moments as well as the various tail eects, is derived through 3.5PN order with respect to the quadrupole formalism. The binary’s orbital phase, whose prior knowledge is crucial for searching and analyzing the signals from inspiralling compact binaries, is deduced from an energy balance argument.

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Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries.

This book treats nonlinear dynamics in both Hamiltonian and dissipative systems. The emphasis is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion, and the dynamical and statistical properties of the dynamics when it is chaotic. The book is intended as a self consistent treatment of the subject at the graduate level and as a reference for scientists already working in the field. It emphasizes both methods of calculation and results. It is accessible to physicists and engineers without training in modern mathematics. The new edition brings the subject matter in a rapidly expanding field up to date, and has greatly expanded the treatment of dissipative dynamics to include most important subjects. It can be used as a graduate text for a two semester course covering both Hamiltonian and dissipative dynamics.

Regular and Chaotic Dynamics

Introduction to Ordinary Differential Equations * Linear Systems and Stability of Nonlinear Systems * Applications * Hyperbolic Theory * Continuation of Periodic Solutions * Homoclinic Orbits, Melnikov?s Method, and Chaos * Averaging * Local Bifurcation * References * Index.

http://www.math.ecnu.edu.cn/~zmwang/teaching/Advanced_ODE-2014-2015/1-Textbook_and_Reference_book/2-Ordinary%20Differential%20Equations%20with%20Applications.pdf

Ordinary Differential Equations with Applications

Close to a transition between different phases a substance can show universal behavior that is independent of the microscopic details and is characterized by power law correlations and critical exponents. In this Colloquium the concepts of criticality and universality are discussed when applied to biological systems and suggest that in some cases these systems can extract functional advantages close to criticality.

Colloquium : Criticality and dynamical scaling in living systems

The article reviews the current status of a theoretical approach to the problem of the emission of gravitational waves by isolated systems in the context of general relativity Part A of the article deals with general post-Newtonian sources The exterior field of the source is investigated by means of a combination of analytic post-Minkowskian and multipolar approximations The physical observables in the far-zone of the source are described by a specific set of radiative multipole moments By matching the exterior solution to the metric of the post-Newtonian source in the near-zone we obtain the explicit expressions of the source multipole moments The relationships between the radiative and source moments involve many non-linear multipole interactions, among them those associated with the tails (and tails-of-tails) of gravitational waves Part B of the article is devoted to the application to compact binary systems We present the equations of binary motion, and the associated Lagrangian and Hamiltonian, at the third post-Newtonian (3PN) order beyond the Newtonian acceleration The gravitational-wave energy flux, taking consistently into account the relativistic corrections in the binary moments as well as the various tail effects, is derived through 35PN order with respect to the quadrupole formalism The binary's orbital phase, whose prior knowledge is crucial for searching and analyzing the signals from inspiralling compact binaries, is deduced from an energy balance argument

/pdf/gravitational-radiation-from-postnewtonian-sources-and-3k5v1g98mj.pdf

Gravitational radiation from postNewtonian sources and inspiraling compact binaries

Delay equations and radiation damping

The long-term nonlinear dynamics of a Keplerian binary system under the combined influences of gravitational radiation damping and external tidal perturbations is analysed. Gravitational radiation reaction leads the binary system towards eventual collapse, while the external periodic perturbations could lead to the ionization of the system via Arnold diffusion. When these two opposing tendencies nearly balance each other, interesting chaotic behaviour occurs which is briefly studied in this paper. It is possible to show that periodic orbits can exist in this system for sufficiently small damping. Moreover, we employ the method of averaging to investigate the phenomenon of capture into resonance.

Gravitational ionization: a chaotic net in the Kepler system

The gravitational ionization of a Keplerian binary system via normally incident periodic gravitational radiation of definite helicity is discussed. The periodic orbits of the planar tidal equation are investigated on the basis of degenerate continuation theory. The relevance of the Kolmogorov‐Arnold‐Moser theory to the question of gravitational ionization is elucidated, and it is conjectured that the process of ionization is closely related to the Arnold diffusion of the perturbed system.

On the ionization of a Keplerian binary system by periodic gravitational radiation

La perturbation a long terme d'un systeme binaire Newtonien par une onde gravitationelle incidente est examinee et mise en relation avec l'ionisation gravitationelle. On etudie les orbites periodiques de l'equation plane des marees et on presente leurs conditions d'existence. La possibilite de l'ionisation d'une orbite Keplerienne par radiation gravitationelle est discutee.

Gravitational ionization : periodic orbits of binary systems perturbed by gravitational radiation

The gravitational ionization of a Keplerian binary system via normally incident periodic gravitational radiation of definite helicity is discussed. The periodic orbits of the planar tidal equation are investigated on the basis of degenerate continuation theory. The relevance of the Kolmogorov-Arnold-Moser theory to the question of gravitational ionization is elucidated, and it is conjectured that the process of ionization is closely related to the Arnold diffusion of the perturbed system.

David G. Retzloff

Papers

Delay equations and radiation damping

Gravitational ionization: a chaotic net in the Kepler system

On the ionization of a Keplerian binary system by periodic gravitational radiation

Gravitational ionization : periodic orbits of binary systems perturbed by gravitational radiation

On the Ionization of a Keplerian Binary System by Periodic Gravitational Radiation