  We study stationary slowly rotating black holes, up to quadratic order in the
spin angular momentum, in dynamical Chern-Simons gravity and shift symmetric
Einstein scalar Gauss-Bonnet gravity, as models of string-inspired gravities.
These gravity theories modify general relativity by introducing dynamical
scalar fields coupled with curvature invariants. We show that the linear time
dependence of the scalar fields is allowed from the stationarity of the
effective stress energy tensors. However, these time dependent scalar fields
yield singular behavior of the metric functions at the black hole horizons, or
they are incompatible with the stationarity of the spacetimes. Thus, these
gravity theories admit only known solutions as regular stationary solutions.
Our results suggest the non-existence of rotating non-circular black holes in
these gravity theories.
