  We performed numerical simulations of general relativistic
magnetohydrodynamics with uniform resistivity to investigatethe occurrence of
magnetic reconnection in a split-monopole magnetic field around a Schwarzschild
black hole. We found that magnetic reconnection happens near the black hole at
its equatorial plane. The magnetic reconnection has a point-like reconnection
region and slow shock waves, as in the Petschek reconnection model. The
magnetic reconnection rate decreases as the resistivity becomes smaller. When
the global magnetic Reynolds number is $10^4$ or larger, the magnetic
reconnection rate increases linearly with time from $2 \tau_{\rm S}$ to $\sim
10 \tau_{\rm S}$ ($\tau_{\rm S}=r_{\rm S}/c, r_{\rm S}$ is the Schwarzschild
radius and $c$ is the speed of light). The linear increase of the reconnection
rate agrees with the magnetic reconnection in the Rutherford regime of the
tearing mode instability.
