Abstract
The Weak Gravity Conjecture arises from the assertion that all extremal black holes, even those which are “classical” in the sense of being very massive, must decay by quantum-mechanical emission of particles or smaller black holes. This is interesting, because some observed astrophysical black holes are on the brink of being extremal — though this is due to rapid rotation rather than a large electric or magnetic charge. The possibility that rotating near-extremal black holes might, in addition to radiating spinning particles, also bifurcate by emitting smaller black holes, has attracted much attention of late. There is, however, a basic question to be answered here: can such a bifurcation be compatible with the second law of thermodynamics? This is by no means clear. Here we show that, if there is indeed such a mechanism for bifurcations of AdS4-Kerr-Newman black holes, then this process can in fact satisfy the second law.
Highlights
Manner has profound ramifications for our general understanding of quantum gravity, as was pointed out in [5, 8]: see for example the recent work of Arkani-Hamed et al [9] on the consequences for the charge/mass ratio of extremal black holes
Extremal black holes have attracted a great deal of theoretical attention of late, but most of the focus has been on the Reissner-Nordström case
Near-extremal astrophysical black holes, are in that state due to rotation
Summary
We will discuss magnetically charged black holes [47], partly because such objects are currently of observational interest [3, 4], but mainly because they are generically close to extremality [2], so that extremal bifurcation is relevant to them. The values of a/L compatible with Censorship fall into two disjoint subsets, and the corresponding black holes cannot “communicate” by any continuous process. They might, be related by a discontinuous, quantum process, and that is precisely what occurs in the course of extremal bifurcation, as we shall see. This in itself does not seem very reasonable; intuitively, it would seem that objects with small masses should be the easiest to create by a quantum process Any such lower bound would be fixed by the asymptotic curvature scale L, which does not seem to be relevant to the local physics. We turn to the question of the classical stability of these black holes
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