  The magnetic reconnection process is analyzed for relativistic
magnetohydrodynamical plasmas around rotating black holes. A simple
generalization of the Sweet-Parker model is used as a first approximation to
the problem. The reconnection rate, as well as other important properties of
the reconnection layer, have been calculated taking into account the effect of
spacetime curvature. Azimuthal and radial current sheet configurations in the
equatorial plane of the black hole have been studied, and the case of small
black hole rotation rate has been analyzed. For the azimuthal configuration, it
is found that the black hole rotation decreases the reconnection rate. On the
other hand, in the radial configuration, it is the gravitational force created
by the black hole mass that decreases the reconnection rate. These results
establish a fundamental interaction between gravity and magnetic reconnection
in astrophysical contexts.
