Black hole perturbation in nondynamical and dynamical Chern-Simons
  gravity
  Chern-Simons gravitational theories are extensions of general relativity in
which the parity is violated due to the Chern-Simons term. We study linear
perturbations on the static and spherically symmetric background spacetime both
for nondynamical and dynamical Chern-Simons theories. We do not make an
assumption that the background Chern-Simons scalar field vanishes, which has
been adopted in the literature. By eliminating nondynamical variables using
their constraint equations, we derive the reduced second order action from
which a set of closed evolution equations containing only dynamical variables
are immediately obtained and therefore the number of propagating degrees of
freedom as well. It is found that ghost is present both for the nondynamical
case and for the dynamical case unless the background Chern-Simons scalar field
vanishes. It is also found that if the background scalar field vanishes, ghost
degrees of freedom are killed and all the modes propagate at the speed of
light.
