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 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.

52 pages, 10 figures

References in corpus (16)

• The Weak Gravity Conjecture in three dimensions
• Charge Orbits of Symmetric Special Geometries and Attractors
• Positivity of Curvature-Squared Corrections in Gravity
• A Universal Relation Between Corrections to Entropy and Extremality
• On some properties of the Attractor Equations
• Thermodynamics of 4D Dilatonic Black Holes and the Weak Gravity Conjecture
• Duality and Axionic Weak Gravity
• On the extremality bound of stringy black holes
• The Black Hole Weak Gravity Conjecture with Multiple Charges
• A New Spin on the Weak Gravity Conjecture
• Duality-invariant extensions of Einstein-Maxwell theory
• More on the Weak Gravity Conjecture via Convexity of Charged Operators
• A NUT Charge Weak Gravity Conjecture from Dimensional Reduction
• Black Holes, Moduli, and Long-Range Forces
• Revisiting the AdS Boson Stars: the Mass-Charge Relations
• Bootstrap bound on extremal Reissner-Nordström black hole in AdS

Cited by in corpus (5)

• The Weak Gravity Conjecture: A Review
• Higher derivative corrections to black brane thermodynamics and the weak gravity conjecture
• Long-Range Forces Between Non-Identical Black Holes With Non-BPS Extremal Limits
• Planar Black Holes as a Route to Understanding the Weak Gravity Conjecture
• Four-derivative Corrections to Minimal Gauged Supergravity in Five Dimensions