  Solutions pertaining to a Kerr black hole with a flat horizon undergoing
gradual rotation are explored in the context of gravitational theories modified
by dynamical Chern-Simons terms with cylindrical metrics, which approach
asymptotically the anti de Sitter spacetime. It is shown that the cross-term of
a metric component is unaffected by the perturbations of the Chern-Simons
scalar independently of whether the dynamical Chern-Simons field equation is
uncharged or charged with an electric field. From this result, it is ensured
that the Chern-Simons scalar field can affect the spaces of the metric that
approach asymptotically the flat spacetime only.
