Growth of resonances and chaos for a spinning test particle in the Schwarzschild background
Abstract
Inspirals of stellarmass compact objects into supermassive black holes are known as extreme mass ratio inspirals. In the simplest approximation, the motion of the compact object is modeled as a geodesic in the spacetime of the massive black hole with the orbit decaying due to radiated energy and angular momentum, thus yielding a highly regular inspiral. However, once the spin of the secondary compact body is taken into account, integrability is broken and prolonged resonances along with chaotic motion appear. We numerically integrate the motion of a spinning test body in the field of a nonspinning black hole and analyze it using various methods. We show for the first time that resonances and chaos can be found even for astrophysically relevant values of the spin of the test body. On the other hand, we devise a method to analyze the growth of the resonances, and we conclude that the prolonged resonances we observe are only caused by terms quadratic in spin and will generally stay very small in the smallmassratio limit. Last but not least, we compute gravitational waveforms by numerically solving the Teukolsky equations in the timedomain and establish that they carry information on the motion's dynamics. In particular, we show that the time series of the gravitational wave strain can be used to discern regular from chaotic motion of the source.
 Publication:

Physical Review D
 Pub Date:
 January 2020
 DOI:
 10.1103/PhysRevD.101.024037
 arXiv:
 arXiv:1911.00414
 Bibcode:
 2020PhRvD.101b4037Z
 Keywords:

 General Relativity and Quantum Cosmology;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 18 pages, 14 figures