  Modified theories of gravity are often built such that they contain general
relativity as a limiting case. This inclusion property implies that the Kerr
metric is common to many families of theories. For example, all analytic $f(R)$
theories with vanishing constant term admit the Kerr solution. In any given
theory, however, the response of the gravitational field to astrophysical
disturbances is tied to the structure of the field equations. As such, even if
black holes are Kerr, the underlying theory can, in principle, be probed
through gravitational distortions. In this paper, we study linear perturbations
of a Kerr black hole in $f(R)$ gravity using the Newman-Penrose formalism. We
show that, as in general relativity, the equations governing the perturbed
metric, which depend on the quadratic term of the function $f$, completely
decouple.
