The Kijowski--Liu--Yau quasi-local mass of the Kerr black hole horizon

TL;DR

This paper computes the quasi-local mass of Kerr black hole horizons across different spins using isometric embedding into hyperbolic space, revealing a non-monotonic mass behavior as spin varies.

Contribution

It introduces a novel application of isometric embedding into hyperbolic space to calculate the quasi-local mass for Kerr black holes at any spin parameter.

Findings

Mass decreases from 2m to 1.76569m as spin increases from 0 to √3/2.

Mass reaches a maximum near spin 0.99907.

Mass approaches 2.01966m for an extremal Kerr black hole.

Abstract

We use the isometric embedding of the spatial horizon of fast rotating Kerr black hole in a hyperbolic space to compute the quasi-local mass of the horizon for any value of the spin parameter $j=J/m^2$. The mass is monotonically decreasing from twice the ADM mass at $j=0$ to $1.76569m$ at $j=\sqrt{3}/2$. It then monotonicaly increases to a maximum around $j=0.99907$, and finally decreases to $2.01966m$ for $j=1$ which corresponds to the extreme Kerr black hole.