Signature of chaos in gravitational waves from a spinning particle

Abstract

A spinning test particle around a Schwarzschild black hole shows a chaotic behavior, if its spin is larger than a critical value. We discuss whether or not some peculiar signature of chaos appears in the gravitational waves emitted from such a system. Calculating the emitted gravitational waves by use of the quadrupole formula, we find that the energy emission rate of gravitational waves for a chaotic orbit is about 10 times larger than that for a circular orbit, but the same enhancement is also obtained by a regular "elliptic" orbit. A chaotic motion is not always enhance the energy emission rate maximally. As for the energy spectra of the gravitational waves, we find some characteristic feature for a chaotic orbit. It may tell us how to find out a chaotic behavior of the system. Such a peculiar behavior, if it will be found, may also provide us some additional informations to determine parameters of a system such as a spin.

An analytic perturbation approach for classical spinning particle dynamics

“…Getting a better detailed sense of how the Møller radius appears due to this perturbation approach may become useful for understanding the precise conditions for a transition into chaotic dynamics, as suggested in previous work [18][19][20][21].…”

“…In particular, the MPD equations lend themselves well to numerical analysis with applications involving gravitational wave generation in a Kerr background [16,17], evidence of deterministic chaos within particle orbital dynamics [18][19][20][21], and particle motion in a Vaidya background with radially infalling radiation [22]. Recently, a first-order perturbative analysis of the MPD equations was developed by Chicone, Mashhoon, and Punsly (CMP) [23], who applied their formalism to the study of rotating plasma clumps in astrophysical jets.…”

Gravitational waves from a chaotic dynamical system

“…In the previous work [17,18], the parameter region for a spinning test particle in which a particle will show chaotic behavior was discussed. We adopt such parameters, e.g.…”

“…It is also important to study chaos in general relativity because the Einstein equations are nonlinear. Many authors have reported chaos in general relativity [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]. As for a realistic astrophysical object, there has been a discussion whether or not chaos occurs in a compact binary system [21,22,23].…”

Gravitational Waves Interacting with a Spinning Charged Particle in the Presence of a Uniform Magnetic Field

“…The dynamics of spinning test particles which are close to massive compact objects was investigated by several authors; this kind of investigation includes, generation of gravitational waves as spinning particles fall into black holes [20,21,22], chaotic behavior of spinning particles in certain space times [23,24,25] and numerical computations for orbital motions in Kerr background [26]. Interesting results regarding the interaction of spinning test matter with gravitational and electromagnetic waves have been obtained by studying the classical motion of the spinning test particles in plane gravitational and electromagnetic field solution to the Einstein-Maxwell equations [27].…”