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arXiv · 2608.12540

Probing the Distribution and Nature of Dark Matter Around Supermassive Black Holes from EMRI and IMRI Gravitational Waves

Jared Fier·Farah Abdelshahed·Lilly Kowalczyk·Zhengfei Lyu·Anzhong Wang
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Abstract

The distribution of dark matter in the immediate vicinity of supermassive black holes remains poorly understood despite its importance for galaxy evolution and precision tests of gravity. Future space-based gravitational-wave observatories offer a unique opportunity to probe this relativistic regime through the inspiral of compact objects into supermassive black holes. Building upon our previously constructed exact Einstein-cloud solutions within General Relativity, we develop a fully relativistic framework to investigate the gravitational-wave signatures of collisionless dark-matter halos surrounding supermassive black holes. The framework provides a unified treatment of orbital dynamics, adiabatic inspiral, accumulated gravitational-wave cycles, waveform phase evolution, signal-to-noise ratio, and waveform mismatch for extreme- and intermediate-mass-ratio inspirals (EMRIs/IMRIs). As a representative application, we specialize the formalism to Model I. We show that relativistic dark-matter halos can produce measurable modifications to the accumulated gravitational-wave cycles, waveform phase, signal-to-noise ratio, and waveform mismatch, leading to consistent conclusions regarding detectability. By separating conservative modifications of the spacetime geometry from dissipative effects due to relativistic dynamical friction, we find that the observable signatures are dominated by the former, while the latter remains negligible for the halo models considered. These results demonstrate that future gravitational-wave observations by LISA and similar missions may provide a powerful probe of the relativistic distribution and physical nature of dark matter around supermassive black holes.

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Jared Fier, Farah Abdelshahed, Lilly Kowalczyk, Zhengfei Lyu, Anzhong Wang. 2026-08-12. Probing the Distribution and Nature of Dark Matter Around Supermassive Black Holes from EMRI and IMRI Gravitational Waves. https://arxiv.org/abs/2608.12540

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