wrote:

[...]

Assuming our universe itself contains black holes, to
model this mathematically, one would presumably have
to start with a set of general relativity equations
for the outer black hole, and find some endomorphic
structure to these, i.e. express them in coordinates
which can be parametrized by other coordinates that
themselves in certain ranges satisfy the original
equations (or at least equations consistent with GR).

"endomorphism" isn't the right word here, because it
implies a composition rule that is carried over by the
mapping.

A better phrase might be "self-similar" transformation.
I believe these are part of the relativity theorists'
armoury, although from what I can gather they are used
currently only to exploit fairly obvious and large scale
symmetries such as overall spherical symmetry rather than
subtle bifurcation properties that would need exploring
to model the situation I described.