  The transfer of energy and angular momentum in the magnetic coupling (MC) of
a rotating black hole (BH) with its surrounding accretion disc is discussed
based on a mapping relation derived by considering the conservation of magnetic
flux with two basic assumptions: (i)the magnetic field on the horizon is
constant, (ii) the magnetic field on the disc surface varies as a power law
with the radial coordinate of the disc. The following results are obtained: (i)
the transfer direction of energy and angular momentum between the BH and the
disc depends on the position of a co-rotation radius relative to the MC region
on the disc, which is eventually determined by the BH spin; (ii) the evolution
characteristics of a rotating BH in the MC process without disc accretion are
depicted in a parameter space, and a series of values of the BH spin are given
to indicate the evolution characteristics; (iii) the efficiency of converting
accreted mass into radiation energy of a BH-disc system is discussed by
considering coexistence of disc accretion and the MC process; (iv) the MC
effects on disc radiation and emissivity index are discussed and it is
concluded that they are consistent with the recent XMM-Newton observation of
the nearby bright Seyfert 1 galaxy MCG-6-30-15 with reference to a variety of
parameters of the BH-disc system.
