Constraining Kerr supermassive black hole properties using gravitational waves from inspiraling stellar-mass binary black holes
We study the capability of future space-based gravitational-wave (GW) detectors to constrain supermassive black hole (SMBH) properties through observations of inspiraling stellar-mass binary black holes (BBHs) orbiting them. Focusing on stable hierarchical triple systems, we model the BBH motion in Kerr spacetime and compute the modulated GW signals using the post Newtonian waveform combined with moving-source transformation. Based on the LISA configuration and second-generation time delay interferometry technology, we estimate parameter uncertainties with the Fisher information matrix. Our results show that the outer semimajor axis has the strongest influence on parameter precision, while the SMBH spin and eccentricity mainly affect their own uncertainties. For high-SNR signals, the SMBH mass and orbital parameters can be measured with relative uncertainties on the order of $10^{-5}$, while the spin magnitude and its orientation can be constrained to within a few percentages. Applying the method to an M87*-like system, GW observations provide more precise measurements of the SMBH mass and spin compared with current electromagnetic observations, highlighting the potential of space-based GW astronomy to probe SMBH properties with high accuracy.