How to observe a non-Kerr spacetime

TL;DR

This paper introduces a criterion based on phase space resonance structures to distinguish gravitational waves from non-Kerr spacetimes, aiding in identifying deviations from classical black hole models.

Contribution

It proposes a novel method utilizing the disintegration of phase space tori and the properties of Birkhoff chains to detect non-Kerr spacetimes in gravitational-wave data.

Findings

The criterion can identify non-Kerr spacetimes through frequency ratio constancy.

Resonance structures in phase space differ between Kerr and non-Kerr backgrounds.

The method provides a new tool for gravitational-wave data analysis.

Abstract

We present a generic criterion which can be used in gravitational-wave data analysis to distinguish an extreme-mass-ratio inspiral into a Kerr background spacetime from one into a non-Kerr background spacetime. The criterion exploits the fact that when an integrable system, such as the system that describes geodesic orbits in a Kerr spacetime, is perturbed, the tori in phase space which initially corresponded to resonances disintegrate so as to form the so called Birkhoff chains on a surface of section, according to the Poincar\'{e}-Birkhoff theorem. The KAM curves of these islands in such a chain share the same ratio of frequencies, even though the frequencies themselves vary from one KAM curve to another inside an island. On the other hand, the KAM curves, which do not lie in a Birkhoff chain, do not share this characteristic property. Such a temporal constancy of the ratio of frequencies during the evolution of the gravitational-wave signal will signal a non-Kerr spacetime which could then be further explored.