  We show that the generic solutions of the Lovelock equations with spherical,
planar or hyperbolic symmetry are locally isometric to the corresponding static
Lovelock black hole. As a consequence, these solutions are locally static: they
admit an additional Killing vector that can either be space-like or time-like,
depending on the position. This result also holds in the presence of an abelian
gauge field, in which case the solutions are locally isometric to a charged
static black hole.
