  Let $G$ be a torsion-free hyperbolic group and $\alpha$ an automorphism of
$G$. We show that there exists a canonical collection of subgroups that are
polynomially growing under $\alpha$, and that the mapping torus of $G$ by
$\alpha$ is hyperbolic relative to the suspensions of the maximal polynomially
growing subgroups under $\alpha$.
