Evidence for the Stability of Extremal Black p-Branes

We investigate the stability of the extremal black p-brane which contains a n-form and a dilaton. We show that the instability due to the s-mode, which was present in the uncharged and non-extremal p-brane, disappears in the extreme case. This is shown to be consistent with an entropy argument which shows that the zero entropy of the extremal black hole is approached more rapidly than the zero entropy of the black p-brane, which would mean an instability would violate the second law of thermodynamics.