Bounding Horizon Area by Angular Momentum, Charge, and Cosmological Constant in 5-Dimensional Minimal Supergravity

We establish a class of area-angular momentum-charge inequalities satisfied by stable marginally outer trapped surfaces in 5-dimensional minimal supergravity which admit a $U(1{)}^2$ symmetry. A novel feature is the fact that such surfaces can have the nontrivial topologies $S^1\times S^2$ and $L(p,q)$. In addition to two angular momenta, they may be characterized by `dipole charge’ as well as electric charge. We show that the unique geometries which saturate the inequalities are the horizon geometries corresponding to extreme black hole solutions. Analogous inequalities which also include contributions from a positive cosmological constant are also presented.