Classical defects in higher-dimensional Einstein gravity coupled to nonlinear $\sigma$-models

Abstract

We construct solutions of higher-dimensional Einstein gravity coupled to nonlinear $\sigma$-model with cosmological constant. The $\sigma$-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 $\sigma$-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 $\Lambda >0$ 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 $\Lambda <0$ 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 ($M_2$, $d{S}_2$, or $Ad{S}_2$) with (D-2)-sphere. We study all possible factorized channels.

accepted for publication in the General Relativity and Gravitation

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• Gravitational field of global monopole within the Eddington-inspired Born-Infeld theory of gravity
• Nonlinear $\sigma$-models in the Eddington-inspired Born-Infeld Gravity
• Higher-dimensional black holes with Dirac-Born-Infeld (DBI) global defects
• Topologically Stable BPS and Non-BPS States in Supersymmetric $\mathcal{N}=2$ Baby-Skyrme Model