Mass and spin coevolution during the alignment of a black hole in a warped accretion disc

In this paper, we explore the gravitomagnetic interaction of a black hole (BH) with a misaligned accretion disc to study BH spin precession and alignment jointly with BH mass and spin parameter evolution, under the assumption that the disc is continually fed, in its outer region, by matter with angular momentum fixed on a given direction. We develop an iterative scheme based on the adiabatic approximation to study the BH-disc coevolution: in this approach, the accretion disc transits through a sequence of quasi-steady warped states (Bardeen-Petterson effect) and interacts with the BH until the BH spin aligns with the outer angular momentum direction. For a BH aligning with a co-rotating disc, the fractional increase in mass is typically less than a few percent, while the spin modulus can increase up to a few tens of percent. The alignment timescale is between ~ 100 thousands and ~ 1 millions years for a maximally rotating BH accreting at the Eddington rate. BH-disc alignment from an initially counter-rotating disc tends to be more efficient compared to the specular co-rotating case due to the asymmetry seeded in the Kerr metric: counter-rotating matter carries a larger and opposite angular momentum when crossing the innermost stable orbit, so that the spin modulus decreases faster and so the relative inclination angle.