Vacuum breakdown around a Kerr black hole surrounded by a magnetic field

Abstract: We present the invariant characterization of the region where vacuum breakdown into electron-positron ($e^+e^-$) pairs occurs due to an overcritical electric field, the dyadoregion, in the case of a Kerr black hole (BH) in the presence of an external, asymptotically uniform test magnetic field aligned with the BH rotation axis, using the Wald solution. We calculate the dyadoregion morphology, the electromagnetic energy available for the pairs, the pair-creation rate, the number density of pairs, the average energy per pair, and their energy density and pressure. These results provide initial conditions for simulating the subsequent dynamics of the pair-produced plasma and astrophysical applications in the context of high-energy transients involving BHs in strong electromagnetic fields.