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Context: Accreting black holes (BHs) may be surrounded by a highly magnetizedplasma threaded by a poloidal magnetic field. Non-thermal flares and highenergy components could originate from a hot, collisionless and nearlyforce-free corona. The jets we often observe from these systems are believed tobe rotation-powered and magnetically-driven.  Aims: We study axisymmetric BH magnetospheres where some magnetic field linesanchored in a surrounding disk can connect to the event horizon of a rotatingBH. We identify the sites of magnetic reconnection within 30 gravitationalradii 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 andof the electromagnetic fields around the BH. The disk is represented by asteady plasma in Keplerian rotation, threaded by a frozen dipolar field.  Results: For prograde disks, twisted open magnetic field lines crossing thehorizon power a Blandford-Znajek jet while beyond a critical distance, openfield lines on the disk are open. In the innermost regions, coupling fieldlines ensure the transfer of significant amounts of angular momentum and energybetween the BH and the disk. From the Y-point at the intersection, a currentsheet 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 thosederived from purely force-free models. Dissipation at the Y-point heats thecorona and provides a physically motivated source of hard X-rays above the diskfor reflection models. Episodic plasmoid ejection might explain millisecondflares observed in Cyg X-1. Particles flowing from the Y-point down to the diskcould produce a hot spot at the footpoint of the outermost closed field line.

Spinning black holes magnetically connected to a Keplerian disk -- Magnetosphere, reconnection sheet, particle acceleration and coronal heating