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The construction of a generic parametrization to describe the spacetimegeometry around astrophysical black hole candidates is an important step totest the Kerr black hole hypothesis. In the last few years, theJohannsen-Psaltis metric has been the most common framework to study possibledeviations 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 accretiondisks. The most relevant finding is that the spacetime geometry around objectsthat look like very fast-rotating Kerr black holes may still have largedeviations from the Kerr solution. This was not the case with theJohannsen-Psaltis metric, which means the latter was missing an important classof non-Kerr spacetimes.

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