  We derive specific properties of electromagnetism when gravitational effects
are not negligible and analyze their impact on new physics at the horizons of
black holes. We show that a neutral configuration of charges in a region of
high redshift, characterized by a large $g^{tt}$, produces a highly localized
electromagnetic field that vanishes just beyond that region. This phenomenon
implies the existence of extensive families of spacetime structures generated
by electromagnetic degrees of freedom that are as compact as black holes. We
construct neutral bound states of extremal black holes in four dimensions and
in five dimensions, where one direction is compact. These geometries are
indistinguishable from a neutral black hole, referred to as distorted
Schwarzschild, except in an infinitesimal region near its horizon where the
entrapped electromagnetic structures start to manifest. The five-dimensional
solutions satisfy various criteria for describing black hole microstructure:
they increase in size with the Newton constant, are as compact as the
Schwarzschild black hole, and have an entropy that scales like $M^2$.
