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

Classical defects in higher-dimensional Einstein gravity coupled to nonlinear $$\sigma$$ σ... We construct solutions of higher-dimensional Einstein gravity coupled to nonlinear $$\sigma$$ σ -model with cosmological constant. The $$\sigma$$ σ -model can be perceived as exterior configuration of a spontaneously-broken $$SO(D-1)$$ S O ( D - 1 ) global higher-codimensional “monopole”. Here we allow the kinetic term of the $$\sigma$$ 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 $$\Lambda >0$$ 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 $$\Lambda <0$$ 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 ( $$M_2$$ M 2 , $$dS_2$$ d S 2 , or $$AdS_2$$ A d S 2 ) with (D-2)-sphere. We study all possible factorized channels. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png General Relativity and Gravitation Springer Journals

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

, Volume 49 (9) – Aug 9, 2017
20 pages

/lp/springer_journal/classical-defects-in-higher-dimensional-einstein-gravity-coupled-to-HZi1B6v00f
Publisher
Springer US
Subject
Physics; Theoretical, Mathematical and Computational Physics; Classical and Quantum Gravitation, Relativity Theory; Differential Geometry; Astronomy, Astrophysics and Cosmology; Quantum Physics
ISSN
0001-7701
eISSN
1572-9532
D.O.I.
10.1007/s10714-017-2278-8
Publisher site
See Article on Publisher Site

### Abstract

We construct solutions of higher-dimensional Einstein gravity coupled to nonlinear $$\sigma$$ σ -model with cosmological constant. The $$\sigma$$ σ -model can be perceived as exterior configuration of a spontaneously-broken $$SO(D-1)$$ S O ( D - 1 ) global higher-codimensional “monopole”. Here we allow the kinetic term of the $$\sigma$$ 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 $$\Lambda >0$$ 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 $$\Lambda <0$$ 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 ( $$M_2$$ M 2 , $$dS_2$$ d S 2 , or $$AdS_2$$ A d S 2 ) with (D-2)-sphere. We study all possible factorized channels.

### Journal

General Relativity and GravitationSpringer Journals

Published: Aug 9, 2017

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations