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Authors: Christopher Eling, Jacob D. Bekenstein

Date: 29 Oct 2008

Abstract: Hawking's area theorem guarantees the monotonic growth of the surface area of any black hole provided the matter and fields interacting with it respect the weak positive energy condition. The theorem does not identify specific effects which make it work in particular situations. We here report a specific gedanken experiment in which the theorem seems to be violated: the dropping of an electrically charged test object from rest at a point close to the horizon and on the symmetry axis of a nearly extreme Kerr black hole. In the parallel experiment involving a magnetically charged Reissner-Nordstrom hole, the analogous violation is defused by taking into account a subtle source of repulsion of the charge: the spinning up of the black hole in the process of bringing the charge down to its dropping point. No such effect is known for the Kerr case; we find the electric self-force of the charge to be insufficient to right matters. After exhaustive analysis of the problem we conclude that some, as yet unknown, classical effect must be responsible for the enforcement of the area theorem.

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