Geometric aspects of Extremal Kerr black hole entropy

TL;DR

This paper explores the geometric reasons behind the zero entropy of extremal Kerr black holes, proposing a discontinuity in spacetime geometry as the key factor.

Contribution

It introduces a geometric perspective linking extremal Kerr black hole properties to a discontinuity explaining their vanishing entropy.

Findings

Zero entropy linked to geometric discontinuity

Extremal Kerr black holes lack bifurcate Killing horizon

Unique geometric features define extremal black hole entropy

Abstract

Extreme Black holes are an important theoretical laboratory for exploring the nature of entropy. We suggest that this unusual nature of the extremal limit could explain the entropy of extremal Kerr black holes. The time-independence of the extremal black hole, the zero surface gravity, the zero entropy and the absence of a bifurcate Killing horizon are all related properties that define and reduce to one single unique feature of the extremal Kerr spacetime. We suggest the presence of a true geometric discontinuity as the underlying cause of a vanishing entropy.