  In the context of the dynamics and stability of black holes in modified
theories of gravity, we derive the Teukolsky equations for massless fields of
all spins in general spherically-symmetric and static metrics. We then compute
the short-ranged potentials associated with the radial dynamics of spin 1 and
spin 1/2 fields, thereby completing the existing literature on spin 0 and 2.
These potentials are crucial for the computation of Hawking radiation and
quasi-normal modes emitted by black holes. In addition to the Schwarzschild
metric, we apply these results and give the explicit formulas for the radial
potentials in the case of charged (Reissner--Nordstr\"om) black holes,
higher-dimensional black holes, and polymerized black holes arising from loop
quantum gravity. These results are in particular relevant and applicable to a
large class of regular black hole metrics. The phenomenological applications of
these formulas will be the subject of a companion paper.
