Repulsive black holes and higher-derivatives

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 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.

Four-derivative Corrections to Minimal Gauged Supergravity in Five Dimensions

“…Of particular note, we found c i coefficients that disagree with a number of results in the literature [27][28][29]31]. However, while we believe the particular c i determined previously are incorrect, the results which they are used to derive are still generally valid as they are predominantly applied to non-rotating, non-dyonic solutions, for which the discrepancy, in the form of (F 2 ) 2 − 2F 4 , vanishes.…”

“…As mentioned in the introduction, this is in conflict with some prior results [27,29,31]. However, support for the present result can be obtained from investigating supersymmetric BMPV black holes, which we turn to next.…”

“…Additional puzzles come from some asymptotically flat solutions like supersymmetric black rings [34] and four-dimensional dyonic STU black holes lifted to five dimensions [31]. Of particular note is that the black ring reduces to the BMPV solution in the limit that the ring radius goes to zero.…”

Long-Range Forces Between Non-Identical Black Holes With Non-BPS Extremal Limits

“…While the WGC and the RFC are clearly related to each other, they are distinct in the presence of scalars [4]. Moreover, studies of black holes in theories with higher derivatives make the difference even more manifest [5], and suggest that the RFC can not be satisfied by the black hole spectrum alone -unlike the WGC, which can [6]. Taking these considerations into account, it is valuable to better understand what else we can extract from the behavior of long-range forces, in order to eventually clarify to what extent the RFC is a useful criterion for constraining EFTs.…”

“…2 In theories with higher derivative corrections this is no longer true. The long-range force between extremal black holes receives corrections and does not generically vanish [5]. 3 We are neglecting O 1 r 3 terms as well as velocity dependent forces.…”