Stability of Bianchi attractors in Gauged Supergravity

TL;DR

This paper investigates the stability of extremal black brane horizons with homogeneous symmetry in five-dimensional gauged supergravity, identifying conditions under which these attractors remain stable against scalar fluctuations.

Contribution

It provides a stability analysis of Bianchi attractors in gauged supergravity, revealing that only certain Bianchi types with specific symmetries satisfy stability conditions.

Findings

Stability requires specific symmetry group restrictions.

Stable attractors are found in models with Lifshitz and Bianchi symmetries.

A concrete example demonstrates the existence of stable attractors.

Abstract

In this paper, we analyse the stability of extremal black brane horizons with homogeneous symmetry in the spatial directions in five dimensional gauged supergravity, under the fluctuations of the scalar fields about their attractor values. We examine the scalar fluctuation equations at the linearised level and demand that the fluctuations vanish as one approaches the horizon. Imposing certain restrictions on the Killing vectors used for gauging we find that the necessary conditions for stability are satisfied only by a subclass of the Bianchi metrics whose symmetry group factorises into a two dimensional Lifshitz symmetry and any homogeneous symmetry group given by the Bianchi classification. We apply these results to a simple example of a gauged supergravity model with one vector multiplet to find the stable attractors.