Exact flavored black $p$-branes and self-gravitating instantons from toroidal black holes with Skyrme hair

Abstract

In this paper, using the maximal embedding of $SU(2)$ into $SU(N)$ in the Euler angles parameterization, we construct a novel family of exact solutions of the Einstein $SU(N)$-Skyrme model. First, we present a hairy toroidal black hole in $D=4$ dimensions. This solution is asymptotically locally anti-de Sitter and is characterized by discrete hair parameters. Then, we perform a dimensional extension of the black hole to obtain black $p$-branes as solutions of the Einstein $SU(N)$-Non-linear sigma model in $D\ge 5$ dimensions. These are homogeneous and topologically protected. Finally we show that, through a Wick rotation of the toroidal black hole, one can construct an exact self-gravitating instanton. The role that the flavor number $N$ plays in the geometry and thermodynamics of these configurations is also discussed.

arXiv comment25 pages, 9 figures, some comments and references added, accepted for publication in Phys. Rev. D

References in corpus (46)

• Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
• Black Strings and p-Branes are Unstable
• Viscosity, Black Holes, and Quantum Field Theory
• The Instability of Charged Black Strings and p-Branes
• Black Strings, Low Viscosity Fluids, and Violation of Cosmic Censorship
• Instabilities of Black Strings and Branes
• Analytic self-gravitating Skyrmions, cosmological bounces and AdS wormholes
• Ricci Flat Black Holes and Hawking-Page Phase Transition in Gauss-Bonnet Gravity and Dilaton Gravity
• Evolution and endpoint of the black string instability: Large D solution
• Hedgehog ansatz and its generalization for self-gravitating Skyrmions
• Generalized Euler Angle Parameterization for U(N) with Applications to SU(N) Coset Volume Measures
• Phases of planar AdS black holes with axionic charge
• Ordered arrays of Baryonic tubes in the Skyrme model in (3+1) dimensions at finite density
• Regular and Black Hole Solutions in the Einstein-Skyrme Theory with Negative Cosmological Constant
• Integrability and chemical potential in the (3+1)-dimensional Skyrme model
• Non-uniform black strings and the critical dimension in the $1/D$ expansion
• On the Euler angles for SU(N)
• Spinning Gravitating Skyrmions
• Regular and Black Hole Skyrmions with Axisymmetry
• Crystals of superconducting Baryonic tubes in the low energy limit of QCD at finite density
• Analytic self-gravitating $4$-Baryons, traversable NUT-AdS wormholes, flat space-time multi-Skyrmions at finite volume and a novel transition in the $SU(3)$-Skyrme model
• Black Hole Skyrmions with Negative Cosmological Constant
• Analytic crystals of solitons in the four dimensional gauged non-linear sigma model
• Exact black strings and p-branes in general relativity
• Spherically Symmetric Solutions of the SU(N) Skyrme Models
• Skyrmion and Skyrme-Black holes in de Sitter spacetime
• Skyrmions, Skyrme stars and black holes with Skyrme hair in five spacetime dimension
• Phase Transition of Electrically Charged Ricci-flat Black Holes
• Black hole and BTZ-black string in the Einstein-SU(2) Skyrme model
• SU(3) Einstein-Skyrme Solitons and Black Holes
• Analytic SU(N) Skyrmions at finite Baryon density
• Spherical Skyrmion black holes as gravitational lenses
• Homogeneous Black Strings in Einstein-Gauss-Bonnet with Horndeski hair and beyond
• Hairy AdS black holes with a toroidal horizon in 4D Einstein-nonlinear $\sigma$-model system
• Analytic multi-Baryonic solutions in the SU(N)-Skyrme model at finite density
• Gravitating superconducting solitons in the (3+1)-dimensional Einstein gauged non-linear sigma-model
• Cooking pasta with Lie groups
• Phase transitions for charged planar solitons in AdS
• Stabilizing Homogeneous Black Strings in AdS
• Lovelock black p-branes with fluxes
• Phase transitions of neutral planar hairy AdS black holes
• Extended Thermodynamics of Self-Gravitating Skyrmions
• Extensions of the generalized hedgehog ansatz for the Einstein-nonlinear $\sigma$-model system: black holes with NUT, black strings and time-dependent solutions
• Analytic meronic black holes, gravitating solitons and higher spins in the Einstein $SU(N)$-Yang-Mills theory
• Parallel waves in Einstein-non linear sigma models
• SU(3) dibaryons in the Einstein-Skyrme model

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