Dyonic black holes supporting nearly-black self-gravitating thin shells

It has recently been revealed that dyonic black-hole spacetimes of a quasitopological non-linear electrodynamic field theory may be characterized by discrete radial regions with the property dg tt(r)/dr=0 in which spherically symmetric massive test shells (Dyson shells with negligible self-gravity) can be supported in static equilibrium states. In the present paper we prove that the dyonic spacetimes of the non-linear electrodynamic field theory may also be characterized by the presence of radial regions with the dimensionless property d[r times g tt(r)]/dr to0+ in which massive self-gravitating thin shells that are on the verge of becoming black holes can be supported in static equilibrium states. Intriguingly, it is proved that the discrete radii of these self-gravitating nearly-black Dyson shells are universal in the sense that they are independent of the masses of the central supporting dyonic compact objects.