The Kijowski–Liu–Yau quasi-local mass of the Kerr black hole horizon * * Dedicated to Gary Gibbons on the occasion of his 75th birthday.

Abstract

Abstract: We use an isometric embedding of the cross-over surface of the outer horizon of a rapidly rotating Kerr black hole in a hyperbolic space to compute the quasi-local mass of the horizon for any allowed value of the spin parameter j = J/m 2. The mass is monotonically decreasing from twice the ADM mass at j = 0 to 1.765 69m at j=3/2 . It then monotonically increases to a maximum around j = 0.999 07, and finally decreases to 2.019 66m for j = 1 which corresponds to the extreme Kerr black hole.