Testing Ghasemi-Nodehi–Bambi spacetime with continuum-fitting method

The continuum-fitting method is the analysis of the thermal spectrum of the geometrically thin and optically thick accretion disk around stellar-mass black holes. A parametrization aiming to test the Kerr nature of astrophysical black holes was proposed in Ghasemi-Nodehi and Bambi in EPJC 76:290, 2016. The metric contains 11 parameters in addition to the mass and spin parameters. One can recover the Kerr case by setting all parameters to one. In this paper, I study the continuum-fitting method in a Ghasemi-Nodehi–Bambi background. I show the impact of each of the parameters on the spectra. I then employ $\chi ^2$ studies and show that using the continuum-fitting method all parameters of Ghasemi-Nodehi–Bambi spacetime are degenerate. However, the parameter $b_9$ can be constrained in the case of a high spin value and the Ghasemi-Nodehi–Bambi black hole as reference. This degeneracy means that the spectra of the Kerr case cannot be distinguished from spectra produced in Ghasemi-Nodehi–Bambi spacetime. This is a problem as regards measuring the spin of astrophysical black holes and constrain possible deviations from the Kerr case of General Relativity.