On Charged Black Holes in Einstein-Weyl-Maxwell Theory

TL;DR

This paper explores charged black hole solutions in Einstein-Weyl-Maxwell theory, revealing two branches of solutions and establishing a lower bound on the charge-to-mass ratio relevant to the Weak Gravity Conjecture.

Contribution

It uncovers the relationship between charged and neutral black holes in Einstein-Weyl-Maxwell theory and calculates a lower bound on the charge-to-mass ratio for RN-like black holes.

Findings

Identified two branches of charged black holes in the theory.

Found one charged black hole branch differs from Reissner-Nordström black holes.

Calculated a lower charge-to-mass ratio bound less than the extremal RN black hole.

Abstract

There exist two branches of static and spherically symmetric black hole solutions in Einstein-Weyl theory: one is the Schwarzschild black hole, and the other is a numerically constructed black hole that bifurcates from the Schwarzschild solution. Similarly, there are two branches of charged black holes in Einstein-Weyl-Maxwell theory. We have uncovered the relationships between the charged black holes and the neutral ones. The two charged black holes branch out from the bifurcation point of the neutral ones once charge is added. We found that one of the charged black holes is entirely different from the Reissner-Nordstr\"om (RN) black hole, while the other is similar to the RN black hole. In particular, the RN-like black hole approaches the RN black hole as the charge increases. We calculated the charge-to-mass ratio of the RN-like charged black hole in the near-extremal limit, and the value is less than that of the extremal RN black hole. Since we consider the higher-derivative Weyl square term as part of the classical gravity theory, rather than as a quantum effect, our result sets a lower bound on the charge-to-mass ratio in the context of the Weak Gravity Conjecture.