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

TL;DR

This work analyzes the classical stability of magnetically charged black $p$-branes in a dilaton–gravity theory and tests the Gubser–Mitra conjecture by comparing dynamical perturbations to local thermodynamics. The authors derive perturbation equations for the dilaton and metric, reduce them to threshold modes with frequency $\Omega=0$, and compute the critical KK mass $m^*$ as a function of the dilaton coupling $a$, brane dimension, and non-extremality. They find distinct stability regimes: for $|a|<a_{ m cr}$ branes stabilize at large non-extremality $\mu$, while for $|a|\ge a_{ m cr}$ instability persists (and may intensify) toward extremality, although extremal branes remain stable; extremal analysis confirms these expectations. Overall, the results corroborate GM in a broad class of magnetically charged branes and reveal rich stability structure driven by the dilaton–gauge coupling.

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.

Figures (3)

• Figure 1: Behavior of threshold masses for black $4$-branes in $D=10$ at various values of $a$ with fixed mass density $M=2^5$. $m^* \simeq 1.581/r_{{H}}\simeq 0.791$ with $r_{{H}}=2$ at $\mu=0$. $\mu_{\rm cr} \simeq 0.818\,(0.8184)$, $0.881\,(0.8814)$, and $1.125\,(1.1254)$ for cases of $a=0$, $1/2$, and $1$, respectively. Here critical values obtained from the GM conjecture are denoted in parentheses. On the righthand side the same data are plotted in terms of the non-extremality parameter $q$. $\mu=6$ corresponds to $q \simeq 0.99996$, $0.99995$, $0.99991$ for $a=3/2$, $2$, $3$.
• Figure 2: Behavior of threshold masses for black $p$-branes with fixed $M$ in $D=10$ in the theory of $|a|=1/2$. At $\mu=0$, $r_{{H}}=2$ and $m^*=\bar{m}^*/r_{{H}} \simeq 1.153$, $1.044$, $0.925$, $0.791$, $0.635$, $0.440$ for $p=1,$$\cdots$, $6$. Critical values for transition points are $q_{\rm cr} \simeq 0.413$, $0.435$, $0.497$, $0.606$, $0.773$, $>0.9993$ for $p=1, \cdots, 6$.
• Figure 3: Critical values of the parameter $\mu$ for various black $p$-branes in $D=10$ at which the threshold mass vanishes $m^*=0$. The solid lines are obtained from the Gubser-Mitra conjecture and the black dots from our numerical results for several values of $a$.