Thermodynamics of a Black Hole with Moon

Abstract

For a Kerr black hole perturbed by a particle on the "corotating" circular orbit (angular velocity equal to that of the unperturbed event horizon), the black hole remains in equilibrium in the sense that the perturbed event horizon is a Killing horizon of the helical Killing field. The associated surface gravity is constant over the horizon and should correspond to the physical Hawking temperature. We calculate the perturbation in surface gravity/temperature, finding it negative: the moon has a cooling effect on the black hole. We also compute the change in horizon angular frequency, which is positive, and the change in surface area/entropy, which vanishes.

8 pages, 4 figures; matches the published version

References in corpus (3)

• Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion
• Dynamical surface gravity
• First Law of Mechanics for Black Hole Binaries with Spins

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• The first law of binary black hole scattering
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