Static black holes without spatial isometries: from AdS multipoles to electrovacuum scalarization

TL;DR

This paper reviews recent findings on static black holes lacking spatial symmetries in four dimensions, highlighting two mechanisms—solitonic limits and scalarization—that produce such non-symmetric black holes with spherical horizons.

Contribution

It introduces a general framework for studying non-symmetric static black holes and identifies two mechanisms—solitonic limits and scalarization—that enable their existence.

Findings

Black holes can lack spatial isometries due to solitonic limits.

Scalarization can produce non-symmetric black holes via zero modes.

The solutions are regular outside horizons of spherical topology.

Abstract

We review recent results on the existence of static black holes without spatial isometries in four spacetime dimensions and propose a general framework for their study. These configurations are regular on and outside a horizon of spherical topology. Two different mechanisms allowing for their existence are identified. The first one relies on the presence of a solitonic limit of the black holes; when the solitons have no spatial isometries, the black holes, being a non-linear bound state between the solitons and a horizon, inherit this property. The second one is related to black hole scalarization, and the existence of zero modes of the scalar field without isometries around a spherical horizon. When the zero modes have no spatial isometries, the backreaction of their non-linear continuation makes the scalarized black holes inherit the absence of spatial continuous symmetries. A number of general features of the solutions are discussed together with possible generalizations.