  The images of supermassive black holes captured by the Event Horizon
Telescope (EHT) collaboration have allowed us to have access to the physical
processes that occur in the vicinity of the event horizons of these objects.
This has enabled us to learn more about the state of rotation of black holes,
about the formation of relativistic jets in their vicinity, about the magnetic
field in the regions close to them, and even about the existence of the photon
ring. Furthermore, black hole imaging gives rise to a new way of testing
general relativity in the strong field regime. This has initiated a line of
research aimed at probing different physical scenarios. While many scenarios
have been proposed in the literature that yield distortion effects that would
be a priori detectable at the resolution achieved by future EHT observations,
the vast majority of those scenarios involve strange objects or exotic matter
content. Here, we consider a less heterodox scenario which, involving
non-exotic matter, in the sense that it satisfies all energy conditions and is
dynamically stable, also leads to a deformation of the black hole shadow. We
consider a specific concentration of non-emitting, relativistic matter of zero
optical depth forming a bubble around the black hole. Due to gravitational
refraction, such a self-interacting -- dark -- matter concentration may produce
sub-annular images, i.e. subleading images inside the photon ring. We calculate
the ray tracing in the space-time geometry produced by such a matter
configuration and obtain the corresponding black hole images. While for
concreteness we restrict our analysis to a specific matter distribution,
modeling the bubble as a thin-shell, effects qualitatively similar to those
described here are expected to occur for more general density profiles.
