Isoperimetric surfaces and area-angular momentum inequality in a rotating black hole in New Massive Gravity

TL;DR

This paper investigates the properties of isoperimetric surfaces in rotating black holes within New Massive Gravity, establishing a link between surface stability and the hair parameter, and deriving an area-angular momentum inequality.

Contribution

It introduces a novel analysis of isoperimetric surfaces in this context and proposes a geometric inequality relating area and angular momentum for these black holes.

Findings

Stability depends on the sign of the hair parameter.

Isoperimetric surfaces help derive an area-angular momentum inequality.

Conjectures extend to more general black holes.

Abstract

We study the existence and stability of isoperimetric surfaces in a family of rotating black holes in New Massive Gravity. We show that the stability of such surfaces is determined by the sign of the hair parameter. We use the isoperimetric surfaces to find a geometric inequality between the area and the angular momentum of the black hole, conjecturing geometric inequalities for more general black holes.