Testing No-Hair Theorem by Quasi-Periodic Oscillations: the quadrupole
  of GRO J1655$-$40
  We perform an observational test of no-hair theorem using quasi-periodic
oscillations within the relativistic precession model. Two well motivated
metrics we apply are Kerr-Q and Hartle-Thorne metrics in which the quadrupole
is the parameter that possibly encodes deviations from the Kerr black hole. The
expressions for the quasi-periodic frequencies are derived before comparing the
models with the observation. We encounter a degeneracy in constraining spin and
quadrupole parameters that makes it difficult to measure their values. In
particular, we here propose a novel test of no-hair theorem by adapting the
Hartle-Thorne metric. It turns out that a Kerr black hole is a good description
of the central object in GRO J1655$-$40 given the present observational
precisions.
