Spatially modulated instabilities of an AdS black hole

TL;DR

This paper investigates instabilities in an Einstein-Maxwell AdS black hole within supergravity, revealing a critical Chern-Simons coupling that induces spatially modulated phases at low temperatures.

Contribution

It demonstrates how gauge and mixed gauge-gravitational Chern-Simons terms cause momentum-dependent instabilities leading to spatially modulated solutions.

Findings

Instability occurs at a threshold Chern-Simons coupling.

A bell-curve phase diagram indicates spatial modulation at low temperatures.

Inclusion of higher derivative terms extends the analysis to quartic order.

Abstract

We analyze instabilities of an Einstein-Maxwell theory obtained from an N=2, D=5 supergravity. The theory admits a gauge Chern-Simons term in presence of which we consider perturbative instability of an AdS black hole solution. We find that the strength of the gauge Chern-Simons coupling saturates the threshold value for which the instability occurs, which we have observed both in the near horizon limit as well as analysis of the normal modes. Inclusion of terms upto fourth order in derivatives admits a mixed gauge-gravitational Chern-Simons term as well. Considering both the Chern-Simons terms, we find that momentum dependent instability sets in below a critical temperature giving rise to a bell-curve phase diagram which implies this would lead to a spatially modulated solution. We have considered all the terms upto quartic order of the derivatives and discuss the possible approach for further analysis.