General relativistic viscous accretion flow around Konoplya-Zhidenko black hole

We investigate the properties of accretion flows around the Konoplya-Zhidenko (KZ) black hole, which is proposed by deforming the Kerr metric with a single deformation parameter to test the no-hair theorem using gravitational wave observations. The dynamical equations describing the general relativistic viscous accreting flow are solved self-consistently to find the transonic accretion solutions in terms of global constants, such as energy ($E$), angular momentum ($\mathcal{L}$), viscosity parameter ($\alpha$), spin ($a_{k}$), and deformation parameter ($\eta_0$). We obtain five distinct types of accretion solutions (O, A, $\text{A}^{\prime}$, W, and I-types), and observe that those solutions are not unique but rather continue to exist for wide range of parameter spaces in the $\mathcal{L}-E$ plane. Furthermore, we find that the viscous accretion flows can harbor shock waves when the relativistic shock conditions are satisfied. Consequently, the shock-induced global accretion solutions are obtained, and the effect of $\eta_0$ on shock properties, such as shock radius ($r_{\rm sh}$) and change in electron temperature ($T_{\rm e}$) across the shock front are investigated. Moreover, we calculate the spectral energy distributions (SEDs) of accretion flow using the relativistic thermal bremsstrahlung emission coefficient and study the modification of SEDs due to the increase of $\eta_0$ for both shock-induced and shock-free solutions. In addition, it has been noticed that the observable quantities, like quasi-periodic oscillation frequency ($\nu_{\rm QPO}$) and bolometric disc luminosity ($L$), are strongly dependent on $\eta_0$. Finally, we phenomenologically show that the KZ black hole is consistent with the high-frequency QPOs, commonly observed in black hole binaries and black hole candidates.