Devoured by a Hairy Gargantua: Probing Massive Scalar Charges with Non-minimal Curvature Coupling with Extreme-Mass-Ratio Inspirals

Abstract

Ultralight scalar fields nonminimally coupled to curvature can endow rotating black holes with stationary hair and alter nearby orbits. Using recently constructed hairy black-hole spacetimes, we model the transition to plunge of an extreme-mass-ratio inspiral. For scalar masses $\mu M=0.01$ and $0.1$ and dimensionless curvature coupling $\zeta =10^{-3},10^{-4}$, we find $\mathcal{O}(10)$ rad of gravitational-wave dephasing relative to general relativity over $\mathcal{O}(10^3)$ orbits. A multimode Fisher forecast at $\mu M=0.2$, where neighbouring hair solutions permit a numerical $\mu$-derivative, suggests that $\zeta$ and $\mu$ could be measured to precisions of $\simeq 0.2\%$ and $0.6$--$1.1\%$, respectively, for a source with signal-to-noise ratio of about 80 in LISA.

6 pages (+9 pages supplementary material), 6 figures, 2 tables