Classical Stability of Charged Black Branes and the Gubser-Mitra Conjecture

TL;DR

This paper studies the classical stability of charged black branes in string theory, revealing how stability depends on the dilaton-gauge coupling and confirming the Gubser-Mitra conjecture's link between thermodynamic and classical stability.

Contribution

It demonstrates the influence of the coupling parameter on black brane stability and extends the Gubser-Mitra conjecture to more general charged black brane solutions.

Findings

Stability varies with the coupling parameter, being stable for small values before extremality.

Large coupling leads to persistent instability, but extremal black branes remain stable.

Classical stability features align with thermodynamic predictions via the Gubser-Mitra conjecture.

Abstract

We have investigated the classical stability of magnetically charged black $p$-brane solutions for string theories that include the case studied by Gregory and Laflamme. It turns out that the stability behaves very differently depending on a coupling parameter between dilaton and gauge fields. In the case of Gregory and Laflamme, it has been known that the black brane instability decreases monotonically as the charge of black branes increases and finally disappears at the extremal point. For more general cases we found that, when the coupling parameter is small, black brane solutions become stable even before reaching to the extremal point. On the other hand, when the coupling parameter is large, black branes are always unstable and moreover the instability does not continue to decrease, but starts to increase again as they approach to the extremal point. However all extremal black branes are shown to be stable even in this case. It has also been shown that main features of the classical stability are in good agreement with the local thermodynamic behavior of the corresponding black hole system through the Gubser-Mitra conjecture. Some implications of our results are also discussed.