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We study the quasinormal modes (QNMs) of a charged scalar field on aReissner-Nordstr\"{o}m-anti-de Sitter (RN-AdS$_{5}$) black hole in the smallradius limit by using the isomonodromic method. We also derive thelow-temperature expansion of the fundamental QNM frequency. Finally, we providenumerical evidence that instabilities appear in the small radius limit forlarge values of the charge of the scalar field.

QNMs of scalar fields on small Reissner-Nordstr\"{o}m-AdS$\mathbf{_5}$ black holes