Journal of High Energy Physics

, 2019:111 | Cite as

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

  • C. Herdeiro
  • I. Perapechka
  • E. Radu
  • Ya. ShnirEmail author
Open Access
Regular Article - Theoretical Physics


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 space-time 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.


Black Holes Sigma Models Solitons Monopoles and Instantons Classical Theories of Gravity 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • C. Herdeiro
    • 1
  • I. Perapechka
    • 2
  • E. Radu
    • 3
    • 4
  • Ya. Shnir
    • 5
    • 6
    Email author
  1. 1.Centro de Astrofísica e Gravitação — CENTRA, Departamento de Física, Instituto Superior Técnico — ISTUniversidade de Lisboa — ULLisboaPortugal
  2. 2.Department of Theoretical Physics and AstrophysicsBelarusian State UniversityMinskBelarus
  3. 3.School of Theoretical PhysicsDublin Institute for Advanced StudiesDublin 4Ireland
  4. 4.CIDMA, Universidade de AveiroAveiroPortugal
  5. 5.BLTP, JINRDubnaRussia
  6. 6.Department of Theoretical PhysicsTomsk State Pedagogical UniversityTomskRussia

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