  Whether a short gamma-ray burst (GRB) is caused by a black hole (BH) or a
neutron star (NS) after the merger of a NS binary is a crucial problem. We
propose a BH model that explains short GRBs with long-lasting activities such
as extended emission and plateau emission up to $\sim10000$ s. To extract the
BH rotational energy, the topological evolution of the magnetic field should
accompany the mass ejection, mass fallback, and magnetic field reconnection.
The observations suggest the magnetic field decay from $\sim10^{14}$ G to
$\sim10^{13} - 10^{11}$ G at the BH, bounded below by the pre-merger strength
and kept constant while the luminosity is constant, and the fallback mass of
$\sim10^{-4} - 10^{-2} M_{\odot}$, comparable to the ejecta mass implied by the
macronova (or kilonova) in GRB 130603B. The BH model has implications for
gravitational waves and the equation of state of NS matter.
