Classical stability of charged black branes and 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 the coupling parameter between the dilaton and gauge fields. In the case of Gregory and Laflamme, it is known that the black brane instability decreases monotonically as the charge of the 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 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 the extremal point. However, all extremal black branes are shown to be stable even in this case. It has also been shown that the 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.