Geometry of the extreme Kerr black holes

TL;DR

This paper explores the geometric features of extreme Kerr black holes, emphasizing the role of Euler characteristic in differentiating between extreme and nonextreme types and linking geometry with thermodynamics.

Contribution

It introduces the Euler characteristic as a key factor in distinguishing extreme Kerr black holes and examines their geometric and thermodynamic relationships.

Findings

Euler characteristic differentiates extreme from nonextreme black holes

Geometrical properties relate to thermodynamic behavior

Distinct topological sectors identified for black hole types

Abstract

Geometrical properties of the extreme Kerr black holes in the topological sectors of nonextreme and extreme configurations are studied. We find that the Euler characteristic plays an essential role to distinguish these two kinds of extreme black holes. The relationship between the geometrical properties and the intrinsic thermodynamics are investigated.