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Low-luminosity supermassive and stellar-mass black holes (BHs) may beembedded in a collisionless and highly magnetized plasma. They show non-thermalflares indicative of efficient dissipative processes in the vicinity of the BH.During NIR flares from the supermassive BH Sagittarius A* (Sgr A*), GRAVITYdetected circular motion and polarization evolution which suggest the presenceof transient synchrotron-emitting hot spots moving around the BH. We study 3Dreconnecting current layers in the magnetosphere of spinning BHs to determinewhether plasma-loaded flux ropes formed near the event horizon could reproducethe hot spot observations and help constraining the BH spin. We perform global3D particle-in-cell simulations in Kerr spacetime of a pair plasma embedded ina strong large-scale magnetic field originating in a disk in prograde Keplerianrotation. A cone-shaped current layer develops which surrounds the twisted openmagnetic field lines threading the event horizon. Magnetic field lines couplingthe disk to the BH inflate and reconnect a few gravitational radii above thedisk. Particles accelerate and accumulate in a few rotating macroscopic fluxropes. Once flux ropes detach, they propagate in the current layer followingwhat appears as a rapidly opening spiral when seen face-on. A single flux ropecarries enough relativistic particles to emit synchrotron radiation at levelssuitable to reproduce the flares' peak-luminosity of Sgr A* but it quicklyfades away as it flows away. Our kinematic analysis of flux ropes' motionfavors a BH spin of 0.65 to 0.8 for Sgr A*. The flares' duration require thatthe underlying magnetic loop seeded in the disk mid-plane has a finite lifetimeand azimuthal extent. In this scenario, the hot spot corresponds to a spinningarc along which multiple reconnection sites power the net emission as fluxropes episodically detach.

Reconnection-driven flares in 3D black hole magnetospheres -- A scenario for hot spots around Sagittarius A*