  Most no-hair theorems involve the assumption that the scalar field is
independent of time. Recently in [Phys. Rev. D90 (2014) 041501(R)] the
existence of time-dependent scalar hair outside a stationary black hole in
general relativity was ruled out. We generalize this work to modified gravities
and non-minimally coupled scalar field with an additional assumption that the
spacetime is axisymmetric. It is shown that in higher-order gravity such as
metric $f(R)$ gravity the time-dependent scalar hair doesn't exist. While in
Palatini $f(R)$ gravity and non-minimally coupled case the time-dependent
scalar hair may exist.
