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Constituted with a massive black hole and a stellar mass compact object,Extreme Mass Ratio Inspiral (EMRI) events hold unique opportunity for the studyof massive black holes, such as by measuring and checking the relations amongthe mass, spin and quadrupole moment of a massive black hole, putting theno-hair theorem to test. TianQin is a planned space-based gravitational waveobservatory and EMRI is one of its main types of sources. It is important toestimate the capacity of TianQin on testing the no-hair theorem with EMRIs. Inthis work, we use the analytic kludge waveform with quadrupole momentcorrections and study how the quadrupole moment can be constrained withTianQin. We find that TianQin can measure the dimensionless quadrupole momentparameter with accuracy to the level of $10^{-5}$ under suitable scenarios. Thechoice of the waveform cutoff is found to have significant effect on theresult: if the Schwarzschild cutoff is used, the accuracy depends strongly onthe mass of the massive black hole, while the spin has negligible impact; ifthe Kerr cutoff is used, however, the dependence on the spin is moresignificant. We have also analyzed the cases when TianQin is observingsimultaneously with other detectors such as LISA.

Science with the TianQin Observatory: Preliminary Results on Testing the No-hair Theorem with EMRI