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Spinning $\sigma$-model solitons in $2+1$ Anti-de Sitter space
High Energy Physics - Theory · Submitted 17 Aug 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim No evidence of a horizon is seen for any of the solutions, and therefore the type $i)$ solutions have naked singularities.
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The abstract, sentence by sentence
We obtain numerical solutions for rotating topological solitons of the nonlinear $\sigma$-model in three-dimensional Anti-de Sitter space. Two types of solutions, $i)$ and $ii)$, are found. The $\sigma$-model fields are everywhere well defined for both types of solutions, but they differ in their space-time domains. Any time slice of the space-time for the type $i)$ solution has a causal singularity, despite the fact that all scalars constructed the curvature tensor are bounded functions. No evidence of a horizon is seen for any of the solutions, and therefore the type $i)$ solutions have naked singularities. On the other hand, the space-time domain, along with the fields, for the type $ii)$ solutions are singularity free. Multiple families of solutions exhibiting bifurcation phenomena are found for this case.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We obtain numerical solutions for rotating topological solitons of the nonlinear $\sigma$-model in three-dimensional Anti-de Sitter space. | contribution 0.95 | 0.97 | 0.16 | asserted 1.00 |
| s1 | Two types of solutions, $i)$ and $ii)$, are found. | result 0.98 | 0.96 | 0.07 | asserted 1.00 |
| s2 | The $\sigma$-model fields are everywhere well defined for both types of solutions, but they differ in their space-time domains. | result 1.00 | 0.90 | 0.08 | asserted 1.00 |
| s3 | Any time slice of the space-time for the type $i)$ solution has a causal singularity, despite the fact that all scalars constructed the curvature tensor are bounded functions. | result 0.99 | 0.88 | 0.23 | asserted 1.00 |
| s4 | No evidence of a horizon is seen for any of the solutions, and therefore the type $i)$ solutions have naked singularities. | interpretation 0.71 | 0.93 | 0.24 | asserted 0.90 |
| s5 | On the other hand, the space-time domain, along with the fields, for the type $ii)$ solutions are singularity free. | result 1.00 | 0.92 | 0.18 | asserted 1.00 |
| s6 | Multiple families of solutions exhibiting bifurcation phenomena are found for this case. | result 1.00 | 0.96 | 0.12 | asserted 1.00 |
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The paper
Original abstract
We obtain numerical solutions for rotating topological solitons of the nonlinear $\sigma$-model in three-dimensional Anti-de Sitter space. Two types of solutions, $i)$ and $ii)$, are found. The $\sigma$-model fields are everywhere well defined for both types of solutions, but they differ in their space-time domains. Any time slice of the space-time for the type $i)$ solution has a causal singularity, despite the fact that all scalars constructed the curvature tensor are bounded functions. No evidence of a horizon is seen for any of the solutions, and therefore the type $i)$ solutions have naked singularities. On the other hand, the space-time domain, along with the fields, for the type $ii)$ solutions are singularity free. Multiple families of solutions exhibiting bifurcation phenomena are found for this case.
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How the literature uses it
4 arXiv papers cite this in 10 sentences
Papers citing it · 4 sentences without a confident label
Uses its method or tool 1 paper
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As the second analytic solution, we then describe a rotating Skyrme-$AdS_5$ black brane with Skyrmion hair which is obtained by utilizing a constraint previously found by one of the current authors [ref] in section [ref].
A New Paradigm for Topological or Rotational Non-Abelian Gauge Fields from Einstein-Skyrme Holography · Introduction · 0.82
Compares with it 1 paper
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It is important to note that Skyrmions appear in a distinct way in [ref] compared to previous approaches by Son/Stephanov and Sakai/Sugimoto which discuss Skyrmions on the field theory side of the gauge/gravity correspondence [ref] .
A New Paradigm for Topological or Rotational Non-Abelian Gauge Fields from Einstein-Skyrme Holography · Introduction · 0.99
Cites it as background 4 papers
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In two recent works, [ref] , [ref] novel classical solutions to gravity coupled to matter were obtained in an asymptotically $AdS$ background, which represent topological solitons and hairy black holes.
Rotating AdS Einstein universes from constrained metrics · Introduction · 0.81
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In [ref] new types of such asymptotically $AdS$ solutions in three space-time dimensions were found for rotating black holes.
A New Paradigm for Topological or Rotational Non-Abelian Gauge Fields from Einstein-Skyrme Holography · Introduction · 0.91
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The contribution of the scalar to the mass of hairy black holes and hairy solitons, and their relation to the boundary conditions of the scalar field, were discussed in [ref] (see also [ref] for various applications in AdS and flat spacetimes), though they typically rely in numerical methods.
Phase transitions of neutral planar hairy AdS black holes · Introduction · 0.99
What it cites
Cites as background 3 papers
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[ref] , [ref] , [ref] , [ref] Here we show the existence of asymptotically $AdS^3$ $σ$-model solitons.
Hairy AdS Solitons · Introduction · 0.81
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[ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] It is of interest to know if the $2+1$ dimensional nonlinear $σ-$model also admits solutions with horizons at finite distances.
Skyrmion Black Hole Hair: Conservation of Baryon Number by Black Holes and Observable Manifestations · Introduction · 0.97
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[ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] It is of interest to know if the $2+1$ dimensional nonlinear $σ-$model also admits solutions with horizons at finite distances.
Black hole Skyrmion in a generalized Skyrme model · Introduction · 0.97
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