Three Body Interactions, Angular Momentum and Black Hole Moduli Spaces

TL;DR

This paper studies the interactions and dynamics of multiple black holes in higher dimensions, revealing connections to quantum field theory models and providing explicit expressions for three-body interactions.

Contribution

It introduces a novel description of spinning black hole interactions using the de Alfaro, Fubini and Furlan model and derives explicit three-body interaction metrics from quantum amplitudes.

Findings

Spinning black holes at small separations are modeled by the de Alfaro, Fubini and Furlan model.

Explicit three-body interaction expressions are obtained from four-dimensional $^3$ theory amplitudes.

The dynamics of three black holes are analyzed in various approximation regimes.

Abstract

We investigate the dynamics of a pair of (4+1)-dimensional black holes in the moduli approximation and with fixed angular momentum. We find that spinning black holes at small separations are described by the de Alfaro, Fubini and Furlan model. For more than two black holes, we find an explicit expression for the three-body interactions in the moduli metric by associating them with the one-loop three-point amplitude of a four-dimensional $\phi^3$ theory. We also investigate the dynamics of a three black hole system in various approximations.