Geometric relations for rotating and charged AdS black holes

We derive mass-independent equations and inequalities for Kerr-Newman-anti-de Sitter black holes. In particular, we obtain an equation that relates electric charge, angular momentum and the areas of the event and Cauchy horizons. An area-angular momentum-charge inequality is derived from this formula, which becomes an equality in the degenerate limit. The same equation is shown to hold for arbitrary degenerate black holes, which might, for example, be surrounded by matter.