  The Einstein-Euler-Heisenberg (EEH) black hole model is an extension of
classical black hole solutions in general relativity, incorporating quantum
electrodynamics (QED) effects via the Euler-Heisenberg Lagrangian. The
Euler-Heisenberg Lagrangian describes the nonlinear corrections to Maxwell's
equations due to virtual electron-positron pair production in a strong
electromagnetic field. When this Lagrangian is coupled with Einstein's field
equations, it leads to modified black hole solutions that took into account
these quantum corrections. In this paper, we investigate the impact of the
screening parameter, acting as an effective dielectric constant endowed in a
vacuum due to such QED effects, on the properties of the rotating and
electrically charged Einstein-Euler-Heisenberg black holes (EEH). To this aim,
we analyzed and discussed findings as to how the screening parameter, being
positive or negative, affects certain black hole properties such as null
regions, shadow cast and its observables, and quasinormal modes (QNMs) relative
to the Kerr and Kerr-Newman cases. We find that the presence of a screened
charge due to the associated QED effects in this screened Maxwell theory might
noticeably alter the properties of black holes, offering insights into the
interplay between gravity and quantum field effects.
