A survey of spinning test particle orbits in Kerr spacetime

TL;DR

This paper surveys the dynamics of spinning test particles in Kerr spacetime, revealing that while chaos can occur mathematically, realistic astrophysical scenarios do not exhibit chaotic behavior, ensuring predictable gravitational wave signals.

Contribution

It provides a comprehensive analysis of chaos in Papapetrou equations for spinning particles in Kerr spacetime, clarifying the physical relevance of chaotic solutions.

Findings

Chaotic solutions exist mathematically but are not physically realistic.

Realistic solutions do not show chaos, ensuring predictable gravitational wave signals.

Chaos is most prominent in eccentric orbits near the stability limit.

Abstract

We investigate the dynamics of the Papapetrou equations in Kerr spacetime. These equations provide a model for the motion of a relativistic spinning test particle orbiting a rotating (Kerr) black hole. We perform a thorough parameter space search for signs of chaotic dynamics by calculating the Lyapunov exponents for a large variety of initial conditions. We find that the Papapetrou equations admit many chaotic solutions, with the strongest chaos occurring in the case of eccentric orbits with pericenters close to the limit of stability against plunge into a maximally spinning Kerr black hole. Despite the presence of these chaotic solutions, we show that physically realistic solutions to the Papapetrou equations are not chaotic; in all cases, the chaotic solutions either do not correspond to realistic astrophysical systems, or involve a breakdown of the test-particle approximation leading to the Papapetrou equations (or both). As a result, the gravitational radiation from bodies spiraling into much more massive black holes (as detectable, for example, by LISA, the Laser Interferometer Space Antenna) should not exhibit any signs of chaos.