### 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 |
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Article number | 64 |

Journal | Journal of High Energy Physics |

Volume | 2014 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2014 Jun |

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### 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), [64]. https://doi.org/10.1007/JHEP06(2014)064