Isolated black holes without Z(2) isometry

A mechanism to construct asymptotically flat, isolated, stationary black hole (BH) spacetimes with no Z(2) (NoZ) isometry is described. In particular, the horizon geometry of such NoZ BHs does not have the usual north-south (reflection) symmetry. We discuss two explicit families of models wherein NoZ BHs arise. In one of these families, we exhibit the intrinsic horizon geometry of an illustrative example by isometrically embedding it in Euclidean 3-space, resulting in an egg-like shaped horizon. This asymmetry leaves an imprint in the NoZ BH phenomenology, for instance in its lensing of light; but it needs not be manifest in the BH shadow, which in some cases can be analytically shown to retain a Z(2) symmetry. Light absorption and scattering due to an isotropic source surrounding a NoZ BH endows it with a non-zero momentum, producing an asymmetry triggered BH rocket effect.