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

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 to the pairs, the pair-creation rate, the pair number density, the average energy per pair, and the pair 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.