Skyrmions, Skyrme stars and black holes with Skyrme hair in five spacetime dimension

Brihaye, Yves; Herdeiro, Carlos; Radu, Eugen; Tchrakian, D. H.

doi:10.1007/jhep11(2017)037

Cited by 20 publications

(38 citation statements)

References 106 publications

(169 reference statements)

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“…But up to now, the effect of BH rotation upon this "hair" had not been considered. In this work, we have shown the existence of solutions of the Skyrme model on the Kerr BH background, as test field solutions -Skerrmions -, and also constructed four dimensional spinning BHs with Skyrme hair, which may be regarded as back reacting Skerrmions (see [65] for higher dimensional spinning BHs with Skyrme hair, where a technical advantage occurs).…”

Section: Discussionmentioning

confidence: 98%

Skyrmions around Kerr black holes and spinning BHs with Skyrme hair

Herdeiro

Perapechka

Radu

et al. 2018

J. High Energ. Phys.

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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.

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Section: Discussionmentioning

confidence: 98%

Skyrmions around Kerr black holes and spinning BHs with Skyrme hair

Herdeiro

Perapechka

Radu

et al. 2018

J. High Energ. Phys.

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“…Furthermore, BPS skyrmions, which saturate the Faddeev-Bogomolny bound, are found in a model consist only of this term and a potential term [21]. Although initially the construction of higher-order term is given for four-dimensional spacetime, a possible generalization in higher dimensional spacetime is demonstrated in [22]. In that paper, they only studied unit skyrmions (static and stationary), with B = 1, since the main goal was to find and study rotating black holes with Skyrme hair in five-dimensional spacetime.…”

Section: Jhep07(2021)090mentioning

confidence: 99%

“…The main purpose of this work is to find other possible BPS skyrmions in the generalized five-dimensional Skyrme model considered in [22]. In particular, we will try to find BPS skyrmions, for any integer B, in some (genuine) submodels of the generalized five-dimensional Skyrme model via the BPS Lagrangian method, which was initially used to find BPS vortices in three-dimensional spacetime models [23].…”

Section: Jhep07(2021)090mentioning

confidence: 99%

BPS Skyrme submodels of the five-dimensional Skyrme model

Fadhilla

Gunara

Atmaja

2021

J. High Energ. Phys.

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In this paper, we search for the BPS skyrmions in some BPS submodels of the generalized Skyrme model in five-dimensional spacetime using the BPS Lagrangian method. We focus on the static solutions of the Bogomolny’s equations and their corresponding energies with topological charge B > 0 is an integer. We consider two main cases based on the symmetry of the effective Lagrangian of the BPS submodels, i.e. the spherically symmetric and non-spherically symmetric cases. For the spherically symmetric case, we find two BPS submodels. The first BPS submodels consist of a potential term and a term proportional to the square of the topological current. The second BPS submodels consist of only the Skyrme term. The second BPS submodel has BPS skyrmions with the same topological charge B > 1, but with different energies, that we shall call “topological degenerate” BPS skyrmions. It also has the usual BPS skyrmions with equal energies, if the topological charge is a prime number. Another interesting feature of the BPS skyrmions, with B > 1, in this BPS submodel, is that these BPS skyrmions have non-zero pressures in the angular direction. For the non-spherically symmetric case, there is only one BPS submodel, which is similar to the first BPS submodel in the spherically symmetric case. We find that the BPS skyrmions depend on a constant k and for a particular value of k we obtain the BPS skyrmions of the first BPS submodel in the spherically symmetric case. The total static energy and the topological charge of these BPS skyrmions also depend on this constant. We also show that all the results found in this paper satisfy the full field equations of motions of the corresponding BPS submodels.

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“…Since the complete scalar equation (10) is a second order linear equation, such trivial boundary condition at the horizon implies that the scalar vanishes everywhere. The equation (7) for N is trivial and, together with the boundary condition at infinity (11), implies that N = 1 everywhere.…”

Section: Black Hole Solutionsmentioning

confidence: 99%

“…Interestingly, considering Skyrme instead of scalar hair one might find spherically symmetric solutions for hairy black holes in five dimensions[11] …”

mentioning

confidence: 99%

Scalar hair around charged black holes in Einstein-Gauss-Bonnet gravity

Grandi¹,

Landea²

2018

Phys. Rev. D

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We explore charged black hole solutions in Einstein-Gauss-Bonnet gravity in five dimensions, with a charged scalar hair. We interpret such hairy black holes as the final state of the superradiant instability previously reported for this system. We explore the relation of the hairy black hole solutions with the non-backreacting quasibound states and scalar clouds, as well as with the boson star solutions. *

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Skyrmions, Skyrme stars and black holes with Skyrme hair in five spacetime dimension

Cited by 20 publications

References 106 publications

Skyrmions around Kerr black holes and spinning BHs with Skyrme hair

Skyrmions around Kerr black holes and spinning BHs with Skyrme hair

BPS Skyrme submodels of the five-dimensional Skyrme model

Scalar hair around charged black holes in Einstein-Gauss-Bonnet gravity

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