  We show that a formalism for analyzing the near-horizon conformal symmetry of
Schwarzschild black holes using a scalar field probe is capable of describing
black hole decay. The equation governing black hole decay can be identified as
the geodesic equation in the space of black hole masses. This provides a novel
geometric interpretation for the decay of black holes. Moreover, this approach
predicts a precise correction term to the usual expression for the decay rate
of black holes.
