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We perform an observational test of no-hair theorem using quasi-periodicoscillations within the relativistic precession model. Two well motivatedmetrics we apply are Kerr-Q and Hartle-Thorne metrics in which the quadrupoleis the parameter that possibly encodes deviations from the Kerr black hole. Theexpressions for the quasi-periodic frequencies are derived before comparing themodels with the observation. We encounter a degeneracy in constraining spin andquadrupole parameters that makes it difficult to measure their values. Inparticular, we here propose a novel test of no-hair theorem by adapting theHartle-Thorne metric. It turns out that a Kerr black hole is a good descriptionof the central object in GRO J1655$-$40 given the present observationalprecisions.

Testing No-Hair Theorem by Quasi-Periodic Oscillations: the quadrupole of GRO J1655$-$40