Spinning gravitating Skyrmions in a generalized Einstein-Skyrme model

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We consider the O(3) non-linear sigma-model, composed of three real scalar fields with a standard kinetic term and with a symmetry breaking potential in four spacetime dimensions. We show that this simple, geometrically motivated model, admits both self-gravitating, asymptotically flat, non-topological solitons and hairy black holes, when minimally coupled to Einstein's gravity, without the need to introduce higher order kinetic terms in the scalar fields action. Both spherically symmetric and spinning, axially symmetric solutions are studied. The solutions are obtained under a ansatz with oscillation (in the static case) or rotation (in the spinning case) in the internal space. Thus, there is symmetry non-inheritance: the matter sector is not invariant under the individual spacetime isometries. For the hairy black holes, which are necessarily spinning, the internal rotation (isorotation) must be synchronous with the rotational angular velocity of the event horizon. We explore the domain of existence of the solutions and some of their physical properties, that resemble closely those of (mini) boson stars and Kerr black holes with synchronised scalar hair in Einstein-(massive, complex)-Klein-Gordon theory.

Section: Ansatzmentioning

confidence: 99%

Gravitating solitons and black holes with synchronised hair in the four dimensional O(3) sigma-model

Herdeiro

Perapechka

Radu

et al. 2019

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“…As found in [20], however, the flat spacetime Skyrmions possess axially symmetric spinning generalizations 1 , which may, moreover, gravitate [21] (see also [22]). The existence of spinning Skyrmions raises the question if four dimensional asymptotically flat spinning BHs with Skyrme hair exist.…”

Section: Introductionmentioning

confidence: 92%

Skyrmions around Kerr black holes and spinning BHs with Skyrme hair

Herdeiro

Perapechka

Radu

et al. 2018

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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.

“…[40]. Spinning gravitating Skyrmions were considered [42,43] and it was further found that the BPS-Skyrme model does not possess spinning Skyrmions [43] -neither in a curved nor in a flat background. More exotic configurations like the gravitating axisymmetric sphalerons in the Einstein-Skyrme model have also been studied [44].…”

Section: Introductionmentioning

confidence: 99%

“…Unfortunately, since neutron stars are expected to possess some amount of spin, which is acquired during a star's core collapse, the BPS-Skyrme model cannot quite be a good approximation due to the instability found in Ref. [43]. In some limit it may give reasonable answers, nevertheless.…”

Section: Introductionmentioning

confidence: 99%

Higher-order Skyrme hair of black holes

Gudnason¹,

Nitta²

2018

Higher-order derivative terms are considered as replacement for the Skyrme term in an Einstein-Skyrme-like model in order to pinpoint which properties are necessary for a black hole to possess stable static scalar hair. We find two new models able to support stable black hole hair in the limit of the Skyrme term being turned off. They contain 8 and 12 derivatives, respectively, and are roughly the Skyrme-term squared and the so-called BPS-Skyrme-term squared. In the twelfth-order model we find that the lower branches, which are normally unstable, become stable in the limit where the Skyrme term is turned off. We check this claim with a linear stability analysis. Finally, we find for a certain range of the gravitational coupling and horizon radius, that the twelfth-order model contains 4 solutions as opposed to 2. More surprisingly, the lowest part of the would-be unstable branch turns out to be the stable one of the 4 solutions.