  A naive introduction of a dependency of the mass of a black hole on the
Schwarzschild time coordinate results in singular behavior of curvature
invariants at the horizon, violating expectations from complementarity. If
instead a temporal dependence is introduced in terms of a coordinate akin to
the river time representation, the Ricci scalar is nowhere singular away from
the origin. It is found that for a shrinking mass scale due to evaporation, the
null radial geodesics that generate the horizon are slightly displaced from the
coordinate singularity. In addition, a changing horizon scale significantly
alters the form of the coordinate singularity in diagonal (orthogonal) metric
coordinates representing the space-time. A Penrose diagram describing the
growth and evaporation of an example black hole is constructed to examine the
evolution of the coordinate singularity.
