Abstract
It is well known that an identical pair of extremal Reissner-Nordström black holes placed a large distance apart will exert no force on each other. In this paper, I establish that the same result holds in a very large class of two-derivative effective theories containing an arbitrary number of gauge fields and moduli, where the appropriate analog of an extremal Reissner-Nordström black hole is a charged, spherically symmetric black hole with vanishing surface gravity or vanishing horizon area. Analogous results hold for black branes.
Highlights
Massless scalar fields with exactly vanishing potentials — i.e., moduli — are ubiquitous in string-derived quantum gravities with unbroken supersymmetry
I establish that the same result holds in a very large class of two-derivative effective theories containing an arbitrary number of gauge fields and moduli, where the appropriate analog of an extremal Reissner-Nordström black hole is a charged, spherically symmetric black hole with vanishing surface gravity or vanishing horizon area
The discrepancy is again explained by the moduli, which alter the external geometry of the black hole and reduce the gauge coupling near its core, avoiding a naked singularity
Summary
Massless scalar fields with exactly vanishing potentials — i.e., moduli — are ubiquitous in string-derived quantum gravities with unbroken supersymmetry. The relationship between quasiextremal and extremal black holes is important for understanding the relationship between the Repulsive Force Conjecture and the Weak Gravity Conjecture [6].1 This will be explored in more detail in a companion paper [10], where a general prescription for determining the mass of an extremal black hole and the extremality bound MBH(Q) ≥ Mext(Q) will be discussed. To obtain my primary result, I will show that static spherically symmetric black hole solutions and static spherically symmetric and worldvolume translation invariant black brane solutions are determined by a set of equations with a universal form at two-derivative order in the derivative expansion Among these equations is a first order (constraint) equation descending from the Einstein equations that fixes the self-force in terms of the product of the surface gravity and the horizon area of the solution.
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