Planar Black Holes as a Route to Understanding the Weak Gravity Conjecture

Understand

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.