  Trapping light in open cavities is a long sought "holy grail" of
nanophotonics. Plasmonic materials may offer a unique opportunity in this
context, as they may fully suppress the radiation loss and enable the
observation of spatially localized light states with infinite lifetime in an
open system. Here, we investigate how the spatial dispersion effects, e.g.,
caused by the electron-electron interactions in a metal, affect the trapped
eigenstates. Heuristically, one may expect that the repulsive-type
electron-electron interactions should act against light localization, and
thereby that they should have a negative impact on the formation of the
embedded eigenstates. Surprisingly, here we find that the nonlocality of the
material response creates new degrees of freedom and relaxes the requirements
for the observation of trapped light. In particular, a zero-permittivity
condition is no longer mandatory and the same resonator shell can potentially
suppress the radiation loss at multiple frequencies.
