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.Introduction.-The rapid conversion of magnetic energy into plasma particle energy through the process of magnetic reconnection is of paramount importance in many astrophysical processes [1]. Magnetospheric substorms, coronal mass ejections, stellar and gamma-ray flares are just a few examples of pheneomena in which magnetic reconnection is thought to play a crucial role.In recent years, significant work has been undertaken to better understand magnetic reconnection in magnetically dominated environments, where relativistic effects become significant [2]. This has led to the generalization of the classical Sweet-Parker and Petschek reconnection models to the special relativistic regime [3,4]. Furthermore, many numerical campaigns have been devoted to the investigation of the reconnection rate [5][6][7][8][9][10][11][12] and the particle acceleration [13][14][15][16][17][18][19][20] in this regime. Relativistic reconnection has been found to be a very efficient mechanism of magnetic energy conversion and particle acceleration, making it a primary candidate to explain nonthermal emissions from pulsar wind nebulae, gamma-ray bursts, and active galactic nuclei.While special relativistic effects on the reconnection process are starting to become clear, the effects related to the spacetime curvature are far less explored and a detailed understanding is lacking. General relativistic magnetohydrodynamic simulations have repeatedly shown the formation of reconnection layers in proximity of blacks holes [21][22][23][24], where spacetime curvature effects can be important. However, the difficulties related to the spatial and temporal resolution of typical reconnection processes have been such to prevent their thorough study.A step forward in the comprehension of magnetic reconnection in curved spacetime could be taken by studying simple generalizations of known theoretical models. It is the purpose of this Letter to develop such theoretical study considering the contribution of the gravitational