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Properties of a thin accretion disk around a rotating non-Kerr black hole

We study the accretion process in the thin disk around a rotating non-Kerr black hole with a deformed parameter and an unbound rotation parameter. Our results show that the presence of the deformed parameter $ε$ modifies the standard properties of the disk. For the case in which the black hole is more oblate than a Kerr black hole, the larger deviation leads to the smaller energy flux, the lower radiation temperature and the fainter spectra luminosity in the disk. For the black hole with positive deformed parameter, we find that the effect of the deformed parameter on the disk becomes more complicated. It depends not only on the rotation direction of the black hole and the orbit particles, but also on the sign of the difference between the deformed parameter $ε$ and a certain critical value $ε_{c}$. These significant features in the mass accretion process may provide a possibility to test the no-hair theorem in the strong field regime in future astronomical observations.