Stability of Massive Gravity Solutions for Holographic Conductivity

TL;DR

This paper analyzes the stability of black brane solutions in non-linear massive gravity theories with broken diffeomorphism invariance, identifying conditions for ghost instabilities that affect holographic conductivity models.

Contribution

It provides a stability analysis of massive gravity black branes, identifying healthy parameter regions and clarifying the origin of instabilities in holographic conductivity studies.

Findings

Identification of ghost instability regions in parameter space

Re-derivation of holographic conductivity results independently of coordinates

Linking instabilities to previous holographic conductivity issues

Abstract

We consider non-linear massive gravity with two St\"uckelberg fields in which the diffeomorphism invariance is broken spontaneously in two of the spacetime directions. This theory admits a charged anti-de Sitter black brane solution and has recently been used in holographic context as a bulk description of a boundary field theory with momentum dissipation. Here we study the stability of the black brane solution. We identify the physical degrees of freedom and determine the healthy regions of the parameter space of the theory. We find that there is a region in parameter space, where the theory suffers from ghost instability. We recognise this as the reason for the instability found in the previous works on holographic conductivity. We also rederive the previous results for the holographic conductivity in a coordinate independent way.