  We study the instability of higher-dimensional rotating anti-de Sitter black
holes through fragmentation. Fragmentation occurs when black holes rotate too
fast to sustain their horizon, and then the black holes are broken into small
pieces. Using this process, we test the stability of AdS black holes and
discover the dynamical upper bounds of the angular momentum and the
cosmological constant. We show that AdS black holes can exist stably within
limited parameter ranges in the general dimensions. The parameter ranges are
obtained numerically in terms of angular momentum and cosmological constant.
