Note on the Cardoso-Pani-Rico parametrization to test the Kerr black hole hypothesis

The construction of a generic parametrization to describe the spacetime geometry around astrophysical black hole candidates is an important step to test the Kerr black hole hypothesis. In the last few years, the Johannsen-Psaltis metric has been the most common framework to study possible deviations from the Kerr solution with present and near future observations. Recently, Cardoso, Pani and Rico have proposed a more general parametrization. The aim of the present paper is to study this new metric in a specific context, namely the thermal spectrum of geometrically thin and optically thick accretion disks. The most relevant finding is that the spacetime geometry around objects that look like very fast-rotating Kerr black holes may still have large deviations from the Kerr solution. This was not the case with the Johannsen-Psaltis metric, which means the latter was missing an important class of non-Kerr spacetimes.