  Canonical energy is a valuable tool for analyzing the linear stability of
black hole spacetimes; positivity of canonical energy for all perturbations
implies mode stability, whereas the failure of positivity for any perturbation
implies instability. Nevertheless, even in the case of $4$-dimensional
Schwarzschild spacetime --- which is known to be stable --- manifest positivity
of the canonical energy is difficult to establish, due to the presence of
constraints on the initial data as well as the gauge dependence of the
canonical energy integrand. Consideration of perturbations generated by a Hertz
potential would appear to be a promising way to improve this situation, since
the constraints and gauge dependence are eliminated when the canonical energy
is expressed in terms of the Hertz potential. We prove that the canonical
energy of a metric perturbation of Schwarzschild that is generated by a Hertz
potential is positive. We relate the energy quantity arising in the linear
stability proof of Dafermos, Holzegel and Rodnianski (DHR) to the canonical
energy of an associated metric perturbation generated by a Hertz potential. We
also relate the Regge-Wheeler variable of DHR to the ordinary Regge-Wheeler and
twist potential variables of the associated perturbation. Since the Hertz
potential formalism can be generalized to a Kerr black hole, our results may be
useful for the analysis of the linear stability of Kerr.
