Note on the effect of a massive accretion disk in the measurements of black hole spins

The spin measurement of black holes has important implications in physics and astrophysics. Regardless of the specific technique to estimate the black hole spin, all the current approaches assume that the spacetime geometry around the compact object is exactly described by the Kerr solution. This is clearly an approximation, because the Kerr metric is a stationary solution of the vacuum Einstein equations. In this paper, we estimate the effect of a massive accretion disk in the measurement of the black hole spin with a simple analytical model. For typical accretion disks, the mass of the disk is completely negligible, even for future more accurate measurements. However, for systems with very massive disks the effect may not be ignored.