Bianchi Attractors: A Classification of Extremal Black Brane Geometries

TL;DR

This paper classifies a broad family of extremal black brane geometries with homogeneous but anisotropic horizons, expanding understanding of their structure and potential dual field theories in gauge/gravity correspondence.

Contribution

It introduces a classification of extremal black brane horizons based on Bianchi types, including new solutions with scaling symmetries in Einstein gravity with gauge fields.

Findings

Classified extremal black branes using Bianchi types.

Found solutions with scaling symmetries in Einstein gravity.

Constructed a complete extremal solution asymptotic to AdS.

Abstract

Extremal black branes are of interest because they correspond to the ground states of field theories at finite charge density in gauge/gravity duality. The geometry of such a brane need not be translationally invariant in the spatial directions along which it extends. A less restrictive requirement is that of homogeneity, which still allows points along the spatial directions to be related to each other by symmetries. In this paper, we find large new classes of homogeneous but anisotropic extremal black brane horizons, which could naturally arise in gauge/gravity dual pairs. In 4+1 dimensional spacetime, we show that such homogeneous black brane solutions are classified by the Bianchi classification, which is well known in the study of cosmology, and fall into nine classes. In a system of Einstein gravity with negative cosmological term coupled to one or two massive Abelian gauge fields, we find solutions with an additional scaling symmetry, which could correspond to the near-horizon geometries of such extremal black branes. These solutions realize many of the Bianchi classes. In one case, we construct the complete extremal solution which asymptotes to AdS space.