Dynamics of spinning test particles in Kerr spacetime

TL;DR

This paper studies the motion of spinning test particles around rotating black holes using Lyapunov exponents to identify chaos, finding chaos in idealized cases but not in realistic astrophysical scenarios, implying stable gravitational wave signals.

Contribution

It applies Lyapunov exponent analysis to spinning particle dynamics in Kerr spacetime, revealing chaos only in unphysical maximally spinning binary limits, not in realistic cases.

Findings

Positive Lyapunov exponents in maximally spinning binaries

No chaos detected for realistic spin parameters

Implication that gravitational waves are stable and predictable

Abstract

We investigate the dynamics of relativistic spinning test particles in the spacetime of a rotating black hole using the Papapetrou equations. We use the method of Lyapunov exponents to determine whether the orbits exhibit sensitive dependence on initial conditions, a signature of chaos. In the case of maximally spinning equal-mass binaries (a limiting case that violates the test-particle approximation) we find unambiguous positive Lyapunov exponents that come in pairs +/- lambda, a characteristic of Hamiltonian dynamical systems. We find no evidence for nonvanishing Lyapunov exponents for physically realistic spin parameters, which suggests that chaos may not manifest itself in the gravitational radiation of extreme mass-ratio binary black-hole inspirals (as detectable, for example, by LISA, the Laser Interferometer Space Antenna).