Stability of the non-extremal enhancon solution I: perturbation equations

TL;DR

This paper investigates the stability of non-extremal enhancon solutions by analyzing linear perturbations, finding no instabilities in the simplest perturbation modes, and formulating the problem through coupled differential equations.

Contribution

It provides a detailed linear stability analysis of non-extremal enhancon solutions, including the derivation of perturbation equations and the identification of stable modes.

Findings

Simple perturbations do not induce instabilities.

The perturbation equations form a consistent set of coupled differential equations.

The analysis suggests stability of the non-extremal enhancon solutions under studied perturbations.

Abstract

We consider the stability of the two branches of non-extremal enhancon solutions. We argue that one would expect a transition between the two branches at some value of the non-extremality, which should manifest itself in some instability. We study small perturbations of these solutions, constructing a sufficiently general ansatz for linearised perturbations of the non-extremal solutions, and show that the linearised equations are consistent. We show that the simplest kind of perturbation does not lead to any instability. We reduce the problem of studying the more general spherically symmetric perturbation to solving a set of three coupled second-order differential equations.