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.
