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

Abstract

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 is not the case with the Johannsen-Psaltis metric, which means the latter is missing an important class of non-Kerr spacetimes.