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

TL;DR

This paper introduces a new class of asymptotically flat, stationary black holes lacking the usual north-south symmetry, with unique horizon geometries and observable effects like asymmetric lensing and potential recoil due to anisotropic light scattering.

Contribution

It presents explicit models of black holes without $ ext{Z}_2$ isometry, including their horizon geometries and phenomenological implications, expanding the understanding of possible black hole symmetries.

Findings

Horizon geometry can be egg-shaped and asymmetric.

Lensing effects reveal asymmetry, but shadows may remain symmetric.

Asymmetric light scattering can produce a recoil (rocket) effect on the black hole.

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.