  An analytic model of the evolution of a rotating black hole (BH) is proposed
by considering the coexistence of disk accretion with the Blandford-Znajek
process. The evolutionary characteristics of the BH are described in terms of
three parameters: the BH spin $a_*$, the ratio $k$ of the angular velocity of
the magnetic field lines to that of the BH horizon and the parameter $\lambda$
indicating the position of the inner edge of the disk. It is shown that the
ratio $k$ being a little greater than 0.5 affects the evolutionary
characteristics of the BH significantly, and the BH spin increases rather than
decreases in its evolutionary process provided that the initial value of the BH
spin is located in an appropriate value range determined by ratio $k$. Our
calculations show that the system of a BH accretion disk with $k=0.6$ might
provide a much higher output energy in a shorter timescale for gamma-ray bursts
than the same system with $k=0.5$.
