### Abstract

Bianchi black branes (black brane solutions with homogeneous but anisotropic horizons classified by the Bianchi type) provide a simple holographic setting with lattice structures taken into account. In the case of holographic superconductor, we have a persistent current with lattices. Accordingly, we expect that in the dual gravity side, a black brane should carry some momentum along a direction of lattice structure, where translational invariance is broken. Motivated by this expectation, we consider whether - and if possible, in what circumstances - a Bianchi black brane can have momentum along a direction of no-translational invariance. First, we show that this cannot be the case for a certain class of stationary Bianchi black brane solutions in the Einstein-Maxwell-dilation theory. Then we also show that this can be the case for some Bianchi VII_{0} black branes by numerically constructing such a solution in the Einstein-Maxwell theory with an additional vector field having a source term. The horizon of this solution admits a translational invariance on the horizon and conveys momentum (and is "rotating" when compactified). However this translational invariance is broken just outside the horizon. This indicates the existence of a black brane solution which is regular but non-analytic at the horizon, thereby evading the black hole rigidity theorem.

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

Article number | 064 |

Journal | Journal of High Energy Physics |

Volume | 2014 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2014 |

### Fingerprint

### Keywords

- AdS-CFT Correspondence
- Gauge-gravity correspondence
- Holography and condensed matter physics (AdS/CMT)

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2014*(6), [064]. https://doi.org/10.1007/JHEP06(2014)064

**Can a stationary Bianchi black brane have momentum along the direction with no translational symmetry?** / Iizuka, Norihiro; Ishibashi, Akihiro; Maeda, Kengo.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2014, no. 6, 064. https://doi.org/10.1007/JHEP06(2014)064

}

TY - JOUR

T1 - Can a stationary Bianchi black brane have momentum along the direction with no translational symmetry?

AU - Iizuka, Norihiro

AU - Ishibashi, Akihiro

AU - Maeda, Kengo

PY - 2014

Y1 - 2014

N2 - Bianchi black branes (black brane solutions with homogeneous but anisotropic horizons classified by the Bianchi type) provide a simple holographic setting with lattice structures taken into account. In the case of holographic superconductor, we have a persistent current with lattices. Accordingly, we expect that in the dual gravity side, a black brane should carry some momentum along a direction of lattice structure, where translational invariance is broken. Motivated by this expectation, we consider whether - and if possible, in what circumstances - a Bianchi black brane can have momentum along a direction of no-translational invariance. First, we show that this cannot be the case for a certain class of stationary Bianchi black brane solutions in the Einstein-Maxwell-dilation theory. Then we also show that this can be the case for some Bianchi VII0 black branes by numerically constructing such a solution in the Einstein-Maxwell theory with an additional vector field having a source term. The horizon of this solution admits a translational invariance on the horizon and conveys momentum (and is "rotating" when compactified). However this translational invariance is broken just outside the horizon. This indicates the existence of a black brane solution which is regular but non-analytic at the horizon, thereby evading the black hole rigidity theorem.

AB - Bianchi black branes (black brane solutions with homogeneous but anisotropic horizons classified by the Bianchi type) provide a simple holographic setting with lattice structures taken into account. In the case of holographic superconductor, we have a persistent current with lattices. Accordingly, we expect that in the dual gravity side, a black brane should carry some momentum along a direction of lattice structure, where translational invariance is broken. Motivated by this expectation, we consider whether - and if possible, in what circumstances - a Bianchi black brane can have momentum along a direction of no-translational invariance. First, we show that this cannot be the case for a certain class of stationary Bianchi black brane solutions in the Einstein-Maxwell-dilation theory. Then we also show that this can be the case for some Bianchi VII0 black branes by numerically constructing such a solution in the Einstein-Maxwell theory with an additional vector field having a source term. The horizon of this solution admits a translational invariance on the horizon and conveys momentum (and is "rotating" when compactified). However this translational invariance is broken just outside the horizon. This indicates the existence of a black brane solution which is regular but non-analytic at the horizon, thereby evading the black hole rigidity theorem.

KW - AdS-CFT Correspondence

KW - Gauge-gravity correspondence

KW - Holography and condensed matter physics (AdS/CMT)

UR - http://www.scopus.com/inward/record.url?scp=84904326644&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84904326644&partnerID=8YFLogxK

U2 - 10.1007/JHEP06(2014)064

DO - 10.1007/JHEP06(2014)064

M3 - Article

AN - SCOPUS:84904326644

VL - 2014

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 6

M1 - 064

ER -