Angular momentum-area proportionality of extremal charged black holes in odd dimensions

TL;DR

This paper explores the relationships between angular momentum and horizon area in extremal charged black holes across different dimensions, revealing how these relationships change with the inclusion of a dilaton field.

Contribution

It demonstrates that the angular momentum-area proportionality varies between solution branches and becomes universally proportional to the horizon area when a dilaton is present.

Findings

Angular momentum is proportional to horizon area on the Myers-Perry branch.

Angular momentum is proportional to horizon angular momentum on the Tangherlini branch.

Including a dilaton makes angular momentum proportional to horizon area universally.

Abstract

Extremal rotating black holes in Einstein-Maxwell theory feature two branches. On the branch emerging from the Myers-Perry solutions their angular momentum is proportional to their horizon area, while on the branch emerging from the Tangherlini solutions their angular momentum is proportional to their horizon angular momentum. The transition between these branches occurs at a critical value of the charge, which depends on the value of the angular momentum. However, when a dilaton is included, the angular momentum is always proportional to the horizon area.