Using a simplified model of a black hole-accretion disk system which is dominated by Poynting flux, the evolution of the central black hole which is supposed to be powering GRB is discussed. It is demonstrated explicitly that there is a lower limit on the angular momentum parameter for a given GRB energy. It is found that the most energetic GRBs can only accommodate relatively rapid-rotating black holes at the center. For a set of GRBs for which the isotropic energies and T_90s are known, the effect of the disk mass and the magnetic field on the horizon are discussed quantitatively. It is found that the magnetic field has little influence on the energy but affects the GRB duration as expected. The role of the disk mass is found to be significant in determining both the energy and the duration.