From Rotating to Charged Black Holes and Back Again

TL;DR

This paper explores whether higher derivative corrections affect the extremality bounds of rotating black holes similarly to charged ones, using mappings to charged solutions and analyzing superradiant instabilities.

Contribution

It extends the Weak Gravity Conjecture analysis to rotating black holes by examining higher derivative corrections and their impact on extremality bounds through solution mappings.

Findings

Sign of corrections to extremality bounds is non-universal.

Superradiant instability persists in extremal limit.

WGC implications depend on the presence of superradiance.

Abstract

The mild form of the Weak Gravity Conjecture (WGC) requires higher derivative corrections to extremal charged black holes to increase their charge-to-mass ratio. This allows decay via emission of a smaller extremal black hole. In this paper, we investigate if similar constraints hold for extremal rotating black holes. We do so by considering the leading higher derivative corrections to the four-dimensional Kerr black hole and five-dimensional Myers-Perry black hole. We use a known mapping of these rotating solutions to a four-dimensional non-rotating dyonic Kaluza-Klein black hole and impose the WGC on this charged solution. Going back again to the rotating solutions, this fixes the sign of the corrections to the rotating extremality bounds. The sign of the corrections is non-universal, depending on the black hole under consideration. We argue that this is not at odds with black hole decay, because of the presence of a superradiant instability that persists in the extremal limit. When this instability is present, the WGC is implied for the four-dimensional charged black hole.