  One version of the Weak Gravity Conjecture requires that it should be
possible for an extremal black hole to emit a smaller black hole: that is, the
original black hole bifurcates. For asymptotically flat and asymptotically AdS
Reissner-Nordstr\"{o}m black holes with spherical event horizons, such a
bifurcation reduces the total classical entropy of the system, and so it is
apparently forbidden by the second law of thermodynamics. It may well be
possible to remedy this by taking other (for example, quantum-gravitational)
effects into account, but it is difficult to understand this in a quantitative
way. In the case of asymptotically AdS Reissner-Nordstr\"{o}m black holes with
\emph{planar} event horizons, however, one can show that bifurcations are
definitely compatible with the second law. (Naked singularities, generated by
the bifurcation, may play an important role here.) Furthermore, in this case
one can exhibit a detailed mechanism explaining precisely why planar black
holes must indeed be unstable (through emission of branes) when they are
sufficiently close to extremality. Thus planar black holes can improve our
understanding of the WGC.
