Isolated black holes without ${\mathbb{Z}}_2$ isometry

Abstract

A mechanism to construct asymptotically flat, isolated, stationary black hole (BH) spacetimes with no ${\mathbb{Z}}_2$ (No$\mathbb{Z}$) isometry is described. In particular, the horizon geometry of such No$\mathbb{Z}$ BHs does not have the usual north-south (reflection) symmetry. We discuss two explicit families of models wherein No$\mathbb{Z}$ 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 No$\mathbb{Z}$ 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 ${\mathbb{Z}}_2$ symmetry. Light absorption and scattering due to an isotropic source surrounding a No$\mathbb{Z}$ BH endows it with a non-zero momentum, producing an asymmetry triggered BH rocket effect.

6 pages, 5 figures; v2. Matches the version to be published in Phys. Rev. D

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