Skyrmions around Kerr black holes and spinning BHs with Skyrme hair

TL;DR

This paper explores solutions of the Einstein-Skyrme model, revealing new rotating black holes with Skyrme hair, including both topological and non-topological sectors, and connecting these solutions to known scalar clouds and flat spacetime Skyrmions.

Contribution

It introduces rotating black hole solutions with Skyrme hair, including non-topological Skerrmions, and analyzes their properties and relation to scalar clouds and flat spacetime Skyrmions.

Findings

Skerrmions can be in equilibrium with Kerr black holes via a synchronization condition.

Non-topological Skerrmions bifurcate from Kerr solutions and relate to scalar clouds.

Backreacted solutions yield rotating black holes with Skyrme hair connecting to Kerr solutions.

Abstract

We study solutions of the Einstein-Skyrme model. Firstly we consider test field Skyrmions on the Kerr background. These configurations -- hereafter dubbed Skerrmions -- can be in equilibrium with a Kerr black hole (BH) by virtue of a synchronisation condition. We consider two sectors for Skerrmions. In the sector with non-zero baryon charge, Skerrmions are akin to the known Skyrme solutions on the Schwarzschild background. These `topological' configurations reduce to flat spacetime Skyrmions in a vanishing BH mass limit; moreoever, they never become "small" perturbations on the Kerr background: the non-linearities of the Skyrme model are crucial for all such Skerrmions. In the non-topological sector, on the other hand, Skerrmions have no analogue on the Schwarzschild background. Non-topological Skerrmions carry not baryon charge and bifurcate from a subset of Kerr solutions defining an existence line. Therein the appropriate truncation of the Skyrme model yield a linear scalar field theory containing a complex plus a real field, both massive and decoupled, and the Skerrmions reduce to the known stationary scalar clouds around Kerr BHs. Moreover, non-topological Skerrmions trivialise in the vanishing BH mass limit. We then discuss the backreaction of these Skerrmions, that yield rotating BHs with synchronised Skyrme hair, which continously connect to the Kerr solution (self-gravitating Skyrmions) in the non-topological (topological) sector. In particular, the non-topological hairy BHs provide a non-linear realisation, within the Skyrme model, of the synchronous stationary scalar clouds around Kerr.