  We have recently proposed a model for a regular black hole, or an
ultra-compact object, that is premised on having maximally negative radial
pressure throughout the entirety of the object's interior. This model can be
viewed as that of a highly entropic configuration of fundamental, closed
strings near the Hagedorn temperature, but from the perspective of an observer
who is ignorant about the role of quantum physics in counteracting against
gravitational collapse. The advantage of this classical perspective is that one
can use Einstein's equations to define a classical geometry and investigate its
stability. Here, we complete the model by studying an important aspect of this
framework that has so far been overlooked: The geometry and composition of the
outermost layer of the ultra-compact object, which interpolates between the
bulk geometry of the object and the standard Schwarzschild vacuum solution in
its exterior region. By imposing a well-defined set of matching conditions, we
find a metric that describes this transitional layer and show that it satisfies
all the basic requirements; including the stability of the object when
subjected to small perturbations about the background solution. In fact, we are
able to show that, at linearized order, all geometrical and matter fluctuations
are perfectly frozen in the transitional layer, just as they are known to be in
the bulk of the object's interior.
