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Particle acceleration by magnetic reconnection is now recognized as an important process in magnetically dominated regions of galactic and extragalactic black hole sources. This process helps to solve current puzzles specially related to the origin of the very high energy flare emission in these sources. In this review, we discuss this acceleration mechanism and show recent analytical studies and multidimensional numerical SRMHD and GRMHD (special and general relativistic magnetohydrodynamical) simulations with the injection of test particles, which help us to understand this process both in relativistic jets and coronal regions of these sources. The very high energy and neutrino emission resulting from the accelerated particles by reconnection is also discussed.

Magnetic reconnection, Cosmic Ray Acceleration and Gamma-Ray emission around Black Holes and Relativistic Jets