Gravitational multipoles from scattering amplitudes in higher dimensions

TL;DR

This paper develops a systematic method to extract gravitational multipole moments from scattering amplitudes across various dimensions, revealing differences in multipole structures and universality breakdowns in higher-dimensional gravity.

Contribution

It introduces a general procedure for deriving multipole data from scattering amplitudes in arbitrary dimensions, highlighting new multipole structures and limitations of minimal coupling.

Findings

In four dimensions, only mass and current multipoles exist.

In five dimensions, stress multipoles emerge, differing from four-dimensional cases.

Minimal coupling theories cannot reproduce Myers-Perry multipole structures.

Abstract

We investigate the gravitational multipole structure derived from scattering amplitudes in both four- and higher-dimensional spacetimes, with particular focus on the five-dimensional case. We develop a systematic procedure to extract multipole data from scattering amplitudes in arbitrary dimensions. In four dimensions, only two independent multipole moments exist: mass and current moments. In this setting, we analyze the coupling of massive spin-1 and spin-3/2 fields to gravity, showing how the quadrupole and octupole structure of the Kerr solution arises from minimally coupled theories. We then extend the analysis to include non-minimal couplings, deriving the most general rotating solution with spin-induced multipoles up to octupole order. In higher dimensions, an additional infinite family of ``stress'' multipole moments arises. Focusing on the five-dimensional case, we consider both a massive vector and a massive antisymmetric tensor coupled to gravity, and show that the resulting quadrupolar structure is qualitatively different: while the vector field produces only a mass quadrupole, the antisymmetric tensor generates only a stress quadrupole. By computing the corresponding stress-energy tensor, we demonstrate that minimally coupled theories fail to reproduce the multipolar structure of the Myers-Perry solution. This provides a direct manifestation of the breakdown of spin universality in higher dimensions.