### Abstract

We discuss the phase transitions between three states of a plasma fluid (plasma ball, uniform plasma tube, and non-uniform plasma tube), which are dual to the corresponding finite energy black objects (black hole, uniform black string, and non-uniform black string) localized in an asymptotically locally AdS space. Adopting the equation of state for the fluid obtained by the Scherk-Schwarz compactification of a conformal field theory, we obtain axisymmetric static equilibrium states of the plasma fluid and draw the phase diagrams with their thermodynamical quantities. By use of the fluid/gravity correspondence, we predict the phase diagrams of the AdS black holes and strings on the gravity side. The thermodynamic phase diagrams of the AdS black holes and strings show many similarities to those of the black hole-black string system in a Kaluza-Klein vacuum. For instance, the critical dimension for the smooth transition from the uniform to non-uniform strings is the same as that in the Kaluza-Klein vacuum in the canonical ensemble. The analysis in this paper may provide a holographic understanding of the relation between the Rayleigh-Plateau and Gregory-Laflamme instabilities via the fluid/gravity correspondence.

Original language | English |
---|---|

Article number | 066 |

Journal | Journal of High Energy Physics |

Volume | 2009 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2009 |

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### Keywords

- AdS-CFT correspondence
- Black holes in string theory
- Gauge-gravity correspondence

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2009*(3), [066]. https://doi.org/10.1088/1126-6708/2009/03/066

**Black hole-black string phase transitions from hydrodynamics.** / Maeda, Keiichi; Miyamoto, Umpei.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2009, no. 3, 066. https://doi.org/10.1088/1126-6708/2009/03/066

}

TY - JOUR

T1 - Black hole-black string phase transitions from hydrodynamics

AU - Maeda, Keiichi

AU - Miyamoto, Umpei

PY - 2009

Y1 - 2009

N2 - We discuss the phase transitions between three states of a plasma fluid (plasma ball, uniform plasma tube, and non-uniform plasma tube), which are dual to the corresponding finite energy black objects (black hole, uniform black string, and non-uniform black string) localized in an asymptotically locally AdS space. Adopting the equation of state for the fluid obtained by the Scherk-Schwarz compactification of a conformal field theory, we obtain axisymmetric static equilibrium states of the plasma fluid and draw the phase diagrams with their thermodynamical quantities. By use of the fluid/gravity correspondence, we predict the phase diagrams of the AdS black holes and strings on the gravity side. The thermodynamic phase diagrams of the AdS black holes and strings show many similarities to those of the black hole-black string system in a Kaluza-Klein vacuum. For instance, the critical dimension for the smooth transition from the uniform to non-uniform strings is the same as that in the Kaluza-Klein vacuum in the canonical ensemble. The analysis in this paper may provide a holographic understanding of the relation between the Rayleigh-Plateau and Gregory-Laflamme instabilities via the fluid/gravity correspondence.

AB - We discuss the phase transitions between three states of a plasma fluid (plasma ball, uniform plasma tube, and non-uniform plasma tube), which are dual to the corresponding finite energy black objects (black hole, uniform black string, and non-uniform black string) localized in an asymptotically locally AdS space. Adopting the equation of state for the fluid obtained by the Scherk-Schwarz compactification of a conformal field theory, we obtain axisymmetric static equilibrium states of the plasma fluid and draw the phase diagrams with their thermodynamical quantities. By use of the fluid/gravity correspondence, we predict the phase diagrams of the AdS black holes and strings on the gravity side. The thermodynamic phase diagrams of the AdS black holes and strings show many similarities to those of the black hole-black string system in a Kaluza-Klein vacuum. For instance, the critical dimension for the smooth transition from the uniform to non-uniform strings is the same as that in the Kaluza-Klein vacuum in the canonical ensemble. The analysis in this paper may provide a holographic understanding of the relation between the Rayleigh-Plateau and Gregory-Laflamme instabilities via the fluid/gravity correspondence.

KW - AdS-CFT correspondence

KW - Black holes in string theory

KW - Gauge-gravity correspondence

UR - http://www.scopus.com/inward/record.url?scp=67649512209&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67649512209&partnerID=8YFLogxK

U2 - 10.1088/1126-6708/2009/03/066

DO - 10.1088/1126-6708/2009/03/066

M3 - Article

AN - SCOPUS:67649512209

VL - 2009

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 3

M1 - 066

ER -