# Stability of Asymptotically Schroedinger RN Black Hole and Superconductivity

## TL;DR

This paper investigates the stability of asymptotically Schrödinger Reissner-Nordstrom black holes, revealing both low and high temperature instabilities that challenge their use as models for non-relativistic superconductors.

## Contribution

It provides a perturbative analysis showing high-temperature instabilities, suggesting limitations in current holographic models of non-relativistic superconductivity.

## Key findings

- Instability at low temperatures consistent with superconductivity models
- Unexpected high-temperature instability in certain operators
- Implications for the dual gauge theory or model validity

## Abstract

We perform a perturbative (near-critical) analysis of the stability of an asymptotically Schroedinger Reissner-Nordstrom black hole with respect to generation of charged scalar hair. We find that apart from the expected instability at low temperatures typical of holographic models of superconductivity, in the presence of certain operators a similar instability appears as well at high temperatures. We propose that the reason for such a phase diagram could be due to peculiar features of the dual gauge theory or the failure of the model to provide a consistent holographic dual of a non-relativistic superconductor.