Integrability of Black Hole Orbits in Maximal Supergravity

TL;DR

This work tests whether two extremal half-BPS black holes in $N=8$ supergravity possess hidden integrable-like symmetries by examining perihelion precession. Using on-shell superspace methods, it computes the leading post-Newtonian corrections and demonstrates a no-triangle property in the one-loop amplitude, which aligns with zero precession at 1PN. The probe-limit analysis via a ten-dimensional brane construction confirms no precession to all orders in velocity for general three-angle charge misalignment. The authors conjecture that hydrogen-like degeneracies persist at all perturbative orders, signaling a deep symmetry structure with potential implications for higher-point amplitudes in this theory.

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.

Figures (2)

• Figure 1: $\theta$ is parametrizing $SO(2)\setminus$SO(3)$/SO(2)$, i.e., the angle between north pole and different SO(2) orbits
• Figure 5: The orbit of an electrically and magnetically charged object is confined to the surface of a cone with half-angle $\theta_0$.