  Often, geometries with horizons offer insights into the intricate
relationships between general relativity and quantum physics. However, some
subtle aspects of gravitating quantum systems might be difficult to ascertain
using static backgrounds, since quantum mechanics incorporates dynamic
measurability constraints (such as the uncertainty principle, etc.).
  For this reason, the behaviors of quantum systems on a dynamic black hole
background are explored in this paper. The velocities and trajectories of
representative outgoing, ingoing, and stationary classical particles are
calculated and contrasted, and the dynamics of simple quantum fields (both
massless and massive) on the space-time are examined. Invariant densities
associated with the quantum fields are exhibited on the Penrose diagram that
represents the excreting black hole.
  Furthermore, a generic approach for the consistent mutual gravitation of
quanta in a manner that reproduces the given geometry is developed. The
dynamics of the mutually gravitating quantum fields are expressed in terms of
the affine parameter that describes local motions of a given quantum type on
the space-time. Algebraic equations that relate the energy-momentum densities
of the quantum fields to Einstein's tensor can then be developed. An example
mutually gravitating system of macroscopically coherent quanta along with a
core gravitating field is demonstrated. Since the approach is generic and
algebraic, it can be used to represent a variety of systems with specified
boundary conditions.
