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Low-luminosity supermassive and stellar-mass black holes (BHs) may be embedded in a collisionless and highly magnetized plasma. They show non-thermal flares indicative of efficient dissipative processes in the vicinity of the BH. During NIR flares from the supermassive BH Sagittarius A* (Sgr A*), GRAVITY detected circular motion and polarization evolution which suggest the presence of transient synchrotron-emitting hot spots moving around the BH. We study 3D reconnecting current layers in the magnetosphere of spinning BHs to determine whether plasma-loaded flux ropes formed near the event horizon could reproduce the hot spot observations and help constraining the BH spin. We perform global 3D particle-in-cell simulations in Kerr spacetime of a pair plasma embedded in a strong large-scale magnetic field originating in a disk in prograde Keplerian rotation. A cone-shaped current layer develops which surrounds the twisted open magnetic field lines threading the event horizon. Magnetic field lines coupling the disk to the BH inflate and reconnect a few gravitational radii above the disk. Particles accelerate and accumulate in a few rotating macroscopic flux ropes. Once flux ropes detach, they propagate in the current layer following what appears as a rapidly opening spiral when seen face-on. A single flux rope carries enough relativistic particles to emit synchrotron radiation at levels suitable to reproduce the flares' peak-luminosity of Sgr A* but it quickly fades away as it flows away. Our kinematic analysis of flux ropes' motion favors a BH spin of 0.65 to 0.8 for Sgr A*. The flares' duration require that the underlying magnetic loop seeded in the disk mid-plane has a finite lifetime and azimuthal extent. In this scenario, the hot spot corresponds to a spinning arc along which multiple reconnection sites power the net emission as flux ropes episodically detach., Comment: Submitted to A&A, comments welcome

Context: Accreting black holes (BHs) may be surrounded by a highly magnetized plasma threaded by a poloidal magnetic field. Non-thermal flares and high energy components could originate from a hot, collisionless and nearly force-free corona. The jets we often observe from these systems are believed to be rotation-powered and magnetically-driven. Aims: We study axisymmetric BH magnetospheres where some magnetic field lines anchored in a surrounding disk can connect to the event horizon of a rotating BH. We identify the sites of magnetic reconnection within 30 gravitational radii depending on the BH spin. Methods: With the fully general relativistic particle-in-cell code GRZeltron, we solve the time-dependent dynamics of the electron-positron pair plasma and of the electromagnetic fields around the BH. The disk is represented by a steady plasma in Keplerian rotation, threaded by a frozen dipolar field. Results: For prograde disks, twisted open magnetic field lines crossing the horizon power a Blandford-Znajek jet while beyond a critical distance, open field lines on the disk are open. In the innermost regions, coupling field lines ensure the transfer of significant amounts of angular momentum and energy between the BH and the disk. From the Y-point at the intersection, a current sheet forms where particle acceleration via magnetic reconnection takes place. We compute the synchrotron images of the current sheet emission. Conclusions: Our estimates for jet power and BH-disk exchanges match those derived from purely force-free models. Dissipation at the Y-point heats the corona and provides a physically motivated source of hard X-rays above the disk for reflection models. Episodic plasmoid ejection might explain millisecond flares observed in Cyg X-1. Particles flowing from the Y-point down to the disk could produce a hot spot at the footpoint of the outermost closed field line., Comment: Submitted to A&A, 27 pages