Skyrmions around Kerr black holes and spinning BHs with Skyrme hair

Abstract

We study solutions of the Einstein-Skyrme model. Firstly we consider test field Skyrmions on the Kerr background. These configurations -hereafter dubbed Skerrmionscan 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.

Chains of boson stars

“…These hairy BHs obey a synchronization condition relating the angular velocity of the event horizon and the boson field frequency. Most studies so far considered only an even parity scalar field; see e.g., [62][63][64][65][66][67][68][69][70][71][72][73][74]. Synchronized hairy BHs with an odd parity scalar field were obtained in [62,63,74].…”

Excited Kerr black holes with scalar hair

“…[11,12], the properties of ergosurfaces and shadows were also investigated. Furthermore, the study of hairy black holes can be extended to the Proca hair case [13], Kerr-Newman BH [14], non-minimal coupling case [15], and spinning BHs with Skyrme hair [16]. Especially, considering the model of gravity coupled to self-interacting scalar field [17,18], one can obtain the solution of Kerr black holes with ultra-light scalar hair.…”

Magnetized accretion disks around Kerr black holes with scalar hair: Constant angular momentum disks

“…1 The solutions studied here are the fundamental states of the minimal Einstein-Klein-Gordon model without self-interactions. Different generalizations can be obtained, including charged [29] and excited states in the same model [30,31], as well as cousin solutions in different scalar [32][33][34][35][36][37][38] or Proca models [39,40].…”