Probing the multipolar structure of Myers-Perry black holes with scattering amplitudes

TL;DR

This paper derives analytic scattering amplitudes for massive scalars off Myers-Perry black holes, revealing their complex multipolar structure and analyzing specific angular momentum configurations in five dimensions.

Contribution

It extends the scattering analysis to Myers-Perry black holes in Kerr-Schild gauge, highlighting their richer multipolar structure compared to four-dimensional black holes.

Findings

Analytic tree-level scattering amplitude derived for Myers-Perry black holes.

Identification of stress and current multipoles in higher-dimensional black holes.

Explicit expressions for scattering in special angular momentum configurations.

Abstract

We discuss the scattering of massive scalar probes off Myers-Perry black holes in the Kerr-Schild gauge. Extending the analysis performed recently for Kerr(-Newman) black holes, we show that the Kerr-Schild gauge allows to write down the tree-level scattering amplitude for Myers-Perry black holes in analytic form. For generic values of the angular momenta, Myers-Perry solutions have a richer multipolar structure compared to their four-dimensional counterparts, because they are characterized by the presence of stress multipoles, together with the more familiar mass and current multipoles. By focusing on the five-dimensional case, we derive the leading eikonal phase from the scattering amplitude and we give an explicit expression for two limiting scenari, namely when the two angular momenta are the same, so that the mass multipoles vanish but still the solution has a non-vanishing stress quadrupole and a current dipole, and when one of the two angular momenta is zero, and correspondingly the stress multipoles vanish similar to the Kerr case.