Testing general relativity using binary extreme-mass-ratio inspirals

Abstract: It is known that massive black holes (MBHs) of $10^{5-7}\,M_\odot$ could capture small compact objects to form extreme-mass-ratio inspirals (EMRIs). Such systems emit gravitational waves (GWs) in the band of the Laser Interferometer Space Antenna (LISA) and are ideal probes of the space-time geometry of MBHs. Recently, we have shown that MBHs could also capture stellar-mass binary black holes (about $10\,M_\odot$) to form binary-EMRIs (b-EMRIs) and, interestingly, a large fraction of the binaries coalesce due to the tidal perturbation by the MBHs. Here we further show that the coalescence could be detected by LISA as glitches in EMRI signals. We propose an experiment to use the multi-band ($10^2$ and $10^{-3}$ Hz) glitch signals to test gravity theories. Our simulations suggest that the experiment could measure the mass and linear momentum lost via GW radiation, as well as constrain the mass of gravitons, to a precision that is one order of magnitude better than the current limit.