Gravitational multipoles from scattering amplitudes in higher dimensions

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.

23 pages, 1 figure

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