Topologically equivalent yet radiatively distinct orbits in EMRI system

TL;DR

This paper shows that in certain exotic black hole spacetimes, multiple bound orbit families can produce distinguishable gravitational wave signals despite having similar topological properties.

Contribution

It demonstrates that multi-well geometries support coexisting orbit branches that generate different gravitational wave signatures, offering a new way to probe strong-field gravity beyond general relativity.

Findings

Multiple orbit branches coexist in dyonic black hole spacetimes.

Orbit branches with same topological indices can produce different gravitational wave signals.

These signatures could be detected by future space-based gravitational wave observatories.

Abstract

Multiple potential wells for massive test particles, allowing distinct families of bound orbits to coexist, are a characteristic feature of certain exotic compact objects beyond general relativity. Taking the dyonic black hole as a representative example, we demonstrate that such multi-well geometries generically support multiple coexisting branches of bound orbits, in contrast to the single-branch behavior observed in the Schwarzschild spacetime. Crucially, the periodic orbits sharing identical rational rotation number, and hence identical topological indices can nevertheless produce \emph{radiatively distinct} gravitational waves in a representative extreme-mass-ratio inspirals: their amplitude modulation and harmonic content differ because each branch spans different regions of spacetime curvature. These ``topologically equivalent yet waveform-distinguishable'' signatures provide a direct observational probe of strong field gravitational dynamics beyond general relativity, potentially accessible to future space-based gravitational wave detectors.