Classical Stability of Black D3-branes

TL;DR

This paper studies the classical stability of charged black D3-branes in type IIB supergravity, revealing a charge-dependent stability transition consistent with thermodynamic predictions and involving specific field fluctuations.

Contribution

It demonstrates the charge-dependent stability behavior of black D3-branes and confirms the Gubser-Mitra conjecture through explicit perturbation analysis.

Findings

Black D3-branes are unstable at low charge density.

Increasing charge density stabilizes the branes, reaching stability at a critical charge.

Stability transition aligns with thermodynamic predictions.

Abstract

We have investigated the classical stability of charged black $D3$-branes in type IIB supergravity under small perturbations. For s-wave perturbations it turns out that black $D3$-branes are unstable when they have small charge density. As the charge density increases for given mass density, however, the instability decreases down to zero at a certain finite value of the charge density, and then black $D3$-branes become stable all the way down to the extremal point. It has also been shown that such critical value at which its stability behavior changes agrees very well with the predicted one by the thermodynamic stability behavior of the corresponding black hole system through the Gubser-Mitra conjecture. Unstable mode solutions we found involve non-vanishing fluctuations of the self-dual five-form field strength. Some implications of our results are also discussed.