  It has been argued several times in the past that the structure of the
entropy formula for general non-extremal asymptotically flat black holes in
four dimensions can be understood in terms of an underlying conformal symmetry.
A recent implementation of this idea, carried out by Cveti\v{c} and Larsen,
involves the replacement of a conformal factor in the original geometry by an
alternative conformal factor in such a way that the near-horizon behavior and
thermodynamic properties of the black hole remain unchanged, while only the
asymptotics or "environment" of the geometry are modified. The solution thus
obtained, dubbed "subtracted geometry", uplifts to an asymptotically
AdS$_{3}\times S^{2}$ black hole in five dimensions, and an AdS/CFT
interpretation is then possible. Building on this intuition we show that, at
least in the static case, the replacement of the conformal factor can be
implemented dynamically by means of an interpolating flow which we construct
explicitly. Furthermore, we show that this flow can be understood as the effect
of irrelevant perturbations from the point of view of the dual two-dimensional
CFT, and we identify the quantum numbers of the operators responsible for the
flow. This allows us to address quantitatively the validity of CFT computations
for these asymptotically flat black holes and provides a framework to
systematically compute corrections to the CFT results.
