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Thermodynamics of a Black Hole with Moon

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arxiv 1210.8444 v3 pith:5PT6D3YT submitted 2012-10-31 gr-qc hep-th

classification gr-qchep-th
keywords horizonblackholesurfaceangularchangeeventgravity
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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.

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