LISA could distinguish dense gas envelopes around Little Red Dot black holes in up to 15 events per 4-year mission

The arXiv preprint models extreme-mass-ratio inspirals through four LRD interior profiles, including quasi-star convection, radiative BH envelopes, and super-Eddington discs. Environmental drag and accretion alter the phase evolution enough to exceed the mismatch threshold of 0.03 against vacuum waveforms for all but co-rotating disc cases when host masses are below 10^5 solar masses. Detectability drops sharply above z=3.9 for 10 solar-mass companions but remains viable for 30 solar-mass ones at lower redshift if virial masses are overestimated by two orders of magnitude.

Current LRD samples contain 14 objects at z>3.9 and 31 at z<0.9; only the latter population yields detectable events under optimistic rate assumptions drawn from galactic nuclei. The analysis flags that plunge captures in dense clusters suppress the rate to 10^-4 events, underscoring the need for electromagnetic priors on nuclear density.

LISA’s ability to probe these environments would test whether LRDs host quasi-stars or radiatively supported envelopes, directly constraining black-hole growth channels at cosmic dawn. Follow-up work should incorporate full general-relativistic hydrodynamics and realistic spin distributions to refine mismatch predictions.

Next steps include cross-matching JWST LRD catalogs with future LISA localization volumes and running injection campaigns with realistic noise curves to quantify parameter-estimation precision on gas density at the innermost stable orbit.