  An Ermakov-Pinney-like equation associated with the scalar wave equation in
curved space-time is here studied. The example of Schwarzschild space-time
considered in the present work shows that this equation can be viewed more as a
model equation, with interesting applications in black hole physics. Other
applications studied involve cosmological space-times (de Sitter) and pulse of
plane gravitational waves. In all these cases the evolution of the
Ermakov-Pinney field seems to be consistent with a rapid blow-up, unlike the
Schwarzschild case where spatially damped oscillations are allowed. Eventually,
the phase function is also evaluated in many of the above space-time models.
