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

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.

9 pages. Dedicated to Gary Gibbons on the occasion of his 75th birthday. Numerical methods used in the paper clarified. Final version, to appear in Classical and Quantum Gravity

References in corpus (4)

• Quasilocal mass in general relativity
• Isometric embeddings into the Minkowski space and new quasi-local mass
• Global embedding of the Kerr black hole event horizon into hyperbolic 3-space
• Photon Boomerang in a Nearly Extreme Kerr Metric

Cited by in corpus (4)

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• Elizabethan vortices
• Properties of Quasi-local mass in binary black hole mergers
• Strong field behavior of Wang-Yau Quasi-local energy