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

TL;DR

This paper derives new area-angular momentum-charge inequalities for stable trapped surfaces in 5D supergravity, including nontrivial topologies and charges, with extremal black hole geometries saturating these bounds.

Contribution

It introduces novel inequalities involving topology, angular momentum, and charges in 5D supergravity, extending previous results to include dipole charge and cosmological constant effects.

Findings

Inequalities hold for surfaces with $S^1 \times S^2$ and $L(p,q)$ topologies.

Extremal black hole geometries saturate the inequalities.

Inclusion of cosmological constant modifies the bounds.

Abstract

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.