Astrophysically Realistic Secondary Spins Trigger Chaos in Schwarzschild Spacetime and Discernible Gravitational Wave Signatures

TL;DR

This paper demonstrates that astrophysically realistic secondary spins can induce chaos in Schwarzschild spacetime, producing distinct gravitational wave signatures detectable by current or future observatories.

Contribution

It shows that chaos persists within realistic spin ranges and introduces a spectral-flatness measure to distinguish chaotic from regular gravitational wave signals.

Findings

Chaos occurs across realistic secondary spin ranges.

Chaotic signals have dense frequency-domain structures.

Small spin changes can switch the system from regular to chaotic.

Abstract

Chaos in extreme-mass-ratio inspirals is often thought to require unrealistically large secondary spins, making its astrophysical relevance uncertain. However, we find that chaos persists across the astrophysically realistic spin range for a spinning secondary orbiting a Schwarzschild black hole. This nonintegrable dynamics leaves clear signatures in the emitted gravitational waves. Nearby regular and chaotic trajectories can remain similar in the time domain and retain broadly aligned dominant spectral peaks, yet chaotic signals develop a much less discrete frequency-domain structure with dense inter-peak power. Furthermore, we introduce a local spectral-flatness measure and find it to be several hundred times larger for the chaotic signal than for the neighboring regular signals. Finally, a change in the secondary spin by as little as \(1\%\) of its maximal physically allowed value can drive the system from regular to chaotic motion and produce distinctive detector-level waveforms.