Repulsive Black Holes and Higher-Derivatives

TL;DR

This paper investigates how higher-derivative corrections and scalar fields affect the long-range forces between charged black holes, revealing conditions under which they can be self-attractive or self-repulsive, challenging existing conjectures.

Contribution

It develops a method to compute higher-derivative corrections to scalar charges and analyzes their impact on black hole interactions in theories with shift symmetries.

Findings

Higher-derivative corrections can lead to self-attractive or self-repulsive black holes.

Some black holes are both superextremal and self-attractive.

No universal conditions allow for self-repulsive black holes in all charge directions.

Abstract

In two-derivative theories of gravity coupled to matter, charged black holes are self-attractive at large distances, with the force vanishing at zero temperature. However, in the presence of massless scalar fields and four-derivative corrections, zero-temperature black holes no longer need to obey the no-force condition. In this paper, we show how to calculate the long-range force between such black holes. We develop an efficient method for computing the higher-derivative corrections to the scalar charges when the two-derivative theory has a shift symmetry, and compute the resulting force in a variety of examples. We find that higher-derivative corrected black holes may be self-attractive or self-repulsive, depending on the value of the Wilson coefficients and the VEVs of scalar moduli. Indeed, we find black hole solutions which are both superextremal and self-attractive. Furthermore, we present examples where no choice of higher-derivative coefficients allows for self-repulsive black hole states in all directions in charge space. This suggests that, unlike the Weak Gravity Conjecture, which may be satisfied by the black hole spectrum alone, the Repulsive Force Conjecture requires additional constraints on the spectrum of charged particles.