  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.
