Integrability of Black Hole Orbits in Maximal Supergravity

TL;DR

This paper investigates the orbital dynamics of extremal black holes in maximal supergravity, finding no perihelion precession and suggesting integrability due to hidden symmetries, using amplitude methods and brane setups.

Contribution

It introduces a novel analysis combining scattering amplitudes and brane models to study black hole orbits in supergravity, revealing no precession and indicating integrability.

Findings

No perihelion precession observed in studied black hole orbits.

Absence of scalar triangle integrals linked to non-precessing orbits.

Methodology simplifies calculations using on-shell superspace.

Abstract

We study the dynamics of a pair of extremal (half-BPS) black holes in $\mathcal{N}=8$ supergravity, as a potentially solvable model of gravitational dynamics. As a diagnosis of hidden symmetries, we ask whether the perihelion of the orbits precesses over time. We consider black hole charge vectors with arbitrary misalignment. First, we use scattering amplitude methods to compute the leading post-Newtonian correction for general mass ratios. This computation is greatly simplified by introducing a suitable on-shell superspace. Second, we study the probe limit to all orders in velocity and Newton's constant through a ten-dimensional brane setup. In all cases we find no precession. We relate this to the absence of scalar triangle integrals.