General Relativity: An Introduction for Physicists · Problem 13.7

The Kerr geometry — Hobson, Efstathiou & Lasenby

Physics · kerr-event-horizon-area

Problem

Show that the proper area of the event horizon r=r+r = r_+ in the Kerr geometry is given by A=4π(r+2+a2).A = 4\pi\left(r_+^2 + a^2\right). Hence show that, for fixed μ\mu, the area AA is a maximum for a=0a = 0. Conversely, for fixed AA, show that μ\mu is a minimum for a=0a = 0. Comment on your results.

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