Black Holes, Moduli, and Long-Range Forces

TL;DR

This paper demonstrates that in a broad class of theories, certain extremal black holes and black branes exert no long-range force on each other, generalizing known results for Reissner-Nordstrom black holes.

Contribution

It extends the no-force condition to a wide range of two-derivative theories with multiple gauge fields and moduli, including black branes.

Findings

Extremal black holes with zero surface gravity exert no force on each other.

The no-force condition applies to black branes as well.

Results hold across various two-derivative effective theories.

Abstract

It is well known that an identical pair of extremal Reissner-Nordstrom 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-Nordstrom black hole is a charged, spherically symmetric black hole with vanishing surface gravity or vanishing horizon area. Analogous results hold for black branes.