Classical defects in higher-dimensional Einstein gravity coupled to nonlinear σ -models

Ilham Prasetyo, Handhika Satrio Ramadhan

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5 Citations (Scopus)


We construct solutions of higher-dimensional Einstein gravity coupled to nonlinear σ-model with cosmological constant. The σ-model can be perceived as exterior configuration of a spontaneously-broken SO(D- 1) global higher-codimensional “monopole”. Here we allow the kinetic term of the σ-model to be noncanonical; in particular we specifically study a quadratic-power-law type. This is some possible higher-dimensional generalization of the Bariola–Vilenkin (BV) solutions with k-global monopole studied recently. The solutions can be perceived as the exterior solution of a black hole swallowing up noncanonical global defects. Even in the absence of comological constant its surrounding spacetime is asymptotically non-flat; it suffers from deficit solid angle. We discuss the corresponding horizons. For Λ > 0 in 4d there can exist three extremal conditions (the cold, ultracold, and Nariai black holes), while in higher-than-four dimensions the extremal black hole is only Nariai. For Λ < 0 we only have black hole solutions with one horizon, save for the 4d case where there can exist two horizons. We give constraints on the mass and the symmetry-breaking scale for the existence of all the extremal cases. In addition, we also obtain factorized solutions, whose topology is the direct product of two-dimensional spaces of constant curvature (M2, dS2, or AdS2) with (D-2)-sphere. We study all possible factorized channels.

Original languageEnglish
Article number115
JournalGeneral Relativity and Gravitation
Issue number9
Publication statusPublished - 1 Sep 2017


  • Black hole
  • Deficit angle
  • Global defects

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