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It has been suggested that there is possibly a class of stellar-mass blackholes (BHs) residing near (distance $\le 10^3 M$) the galactic center massiveblack hole, Sgr A*. Possible formation scenarios include the mass segregationof massive stellar-mass black holes and/or the disk migration if there was anactive accretion flow near Sgr A* within $\mathcal{O}(10)$ Myr. In this work,we explore the application of this type of objects as sources of space-bornegravitational wave detectors, such as Laser Interferometer Space Antenna(LISA). We find it is possible to probe the spin of Sgr A* based on theprecession of the orbital planes of these stellar-mass black holes movingaround Sgr A*. We also show that the dynamical friction produced by accumulatedcold dark matter near Sgr A* generally produces small measurable phase shift inthe gravitational waveform. In the case that there is an axion cloud near SgrA*, the dynamical friction induced modification to gravitational waveform ismeasurable only if the mass of the axion field is in a narrow range of the massspectrum. Gravitational interaction between the axion cloud and thestellar-mass black holes may introduce additional precession around the spin ofSgr A*. This additional precession rate is generally weaker than thespin-induced Lense-Thirring precession rate, but nevertheless may contaminatethe spin measurement in a certain parameter regime. At last, we point out thatthe multi-body gravitational interaction between these stellar-mass black holesgenerally causes negligible phase shift during the LISA lifetime.

Science Potential for Stellar-mass Black Holes as Neighbors of Sgr A*