  We study the stability of extreme Reissner-Nordstr\"om-AdS black hole under
massless scalar perturbations. We show that the perturbation on the horizon of
the extreme Reissner-Nordstr\"om-AdS black hole experiences a power-law decay,
instead of an exponential decay as observed in the nonextreme AdS black hole.
On the horizon of the extreme Reissner-Nordstr\"om-AdS black hole, the blow up
happens at lower order derivative of the scalar field compared with that of the
extreme Reissner-Nordstr\"om black hole, which shows that extreme AdS black
holes tend to instability in comparison to black holes in asymptotic flat
space-times.

High Energy Physics - Theory;General Relativity and Quantum Cosmology