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

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.