Quasi-periodic oscillations as a tool for testing the Kerr metric: A comparison with gravitational waves and iron line

QPOs are a common feature in the X-ray power density spectrum of black hole binaries and a potentially powerful tool to probe the spacetime geometry around these objects. Here we discuss their constraining power to test the Kerr black hole hypothesis within the relativistic precession model. We compare our results with the constraints that can be obtained from gravitational waves and iron line. We find that QPOs may provide very precise measurements, but they are strongly affected by parameter degeneracy, and it is difficult to test the Kerr metric with this approach in the absence of independent observations to constrain the mass or the spin.