Gravitational waves from a chaotic dynamical system

Abstract

To investigate how chaos affects gravitational waves, we study the gravitational waves from a spinning test particle moving around a Kerr black hole, which is a typical chaotic system. To compare the result with those in non-chaotic dynamical system, we also analyze a spinless test particle, which orbit can be complicated in the Kerr back ground although the system is integrable. We estimate the emitted gravitational waves by the multipole expansion of a gravitational field. We find a striking difference in the energy spectra of the gravitational waves. The spectrum for a chaotic orbit of a spinning particle, contains various frequencies, while some characteristic frequencies appear in the case of a spinless particle.

1/ffluctuations in spinning-particle motions around a Schwarzschild black hole

“…In the chaotic systems we cannot predict the state in the future exactly [1,2]. Such chaotic behaviors have also been found in some relativistic systems [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]. For example, in Schwarzschild spacetime, the motions of a spinning test particle can be chaotic [13].…”

Recurrence analysis as a tool to study chaotic dynamics of extreme mass ratio inspiral in signal with noise

“…For example, the correlation between the spacetime perturbation modes and the components of the trajectory is implied in Ref. 3 and explicitly shown in Figs. 8 and 9 of Ref.…”

“…If the system is not integrable, then non-linear phenomena like chaos and prolonged resonances will appear. 3,4 However, the current template banks do not include such scenarios, which means that in such cases matched filtering would fail. In fact, the standard adiabatic approximation neglects various factors leading to non-integrability.…”

“…3 First they investigated whether the waveforms resulting from a regular and a chaotic orbit bear any significant differences and they found that the respective waveforms look similar. Then they applied a Fourier transform on the waveforms to obtain the corresponding energy spectra.…”

Universality in chaos of particle motion near black hole horizon

“…Classic examples include various motion of a particle orbiting around black holes (for example, see [47,48] and references therein). In particular, it would leave an imprint on gravitational wave emitted from it [49][50][51]. Observation of gravitational wave, which was recently realized by LIGO experiment [52,53], might be able to detect such chaotic behavior around black holes.…”