A note on degeneracy, marginal stability and extremality of black hole horizons

TL;DR

This paper explores the relationship between black hole horizon degeneracy, marginal stability, and a specific geometric relation between area and angular momentum, extending known equivalences under certain energy conditions.

Contribution

It extends the equivalence between horizon degeneracy and marginal stability to include a geometric relation between area and angular momentum for stationary axisymmetric black holes.

Findings

Established the equivalence under the dominant energy condition.

Connected degeneracy and marginal stability with the A=8π|J| relation.

Applicable to sections characterized as strictly future stable marginally outer trapped surfaces.

Abstract

Given a stationary axisymmetric black hole horizon admitting a section characterised as a strictly future stable marginally outer trapped surface, we extend the equivalence between the notions of horizon degeneracy and marginal stability to the fulfillment, under the dominant energy condition, of the A=8\pi |J| geometric relation between the area $A$ and the angular momentum J of a horizon section.