High-spin and high-boost Magnus effect in Kerr-Schild coordinates

Investigate the Magnus effect from dark matter around spinning Kerr black holes in Kerr-Schild coordinates in challenging high-spin and high-boost regimes, including cases in which the sign of the Magnus effect reverses.

Background

The paper develops a coordinate-transformation framework for extracting dynamical-friction diagnostics in boosted Kerr-Schild coordinates and validates it for a non-spinning black hole. The authors identify spinning Kerr black holes as an important application because the spinning Kerr-Schild metric is analytic, whereas the boosted quasi-isotropic metric used in earlier work lacks a closed form and requires some derivatives to be evaluated numerically on the grid.

The proposed extension is motivated particularly by regimes of high spin and high boost, where previous calculations found that the Magnus effect can reverse sign. The paper does not study these cases and explicitly defers their investigation to future work.

References

In the future, the most useful application of this approach is to the case of spinning Kerr black holes in Kerr-Schild coordinates, in particular for calculations of the Magnus effect from dark matter around black holes, as was done in . In this case the spinning Kerr-Schild metric is analytic, whereas the boosted quasi-isotropic version used in did not have a closed form and some derivatives needed to be evaluated numerically from a metric stored on the grid. The use of Kerr-Schild coordinates should significantly reduce the cost and accuracy for a given resolution, which would allow us to push into more challenging regimes of high spins and high boosts, where the sign of the Magnus effect was found to reverse in some cases. We leave the study of such cases to future work.

— Relativistic dynamical friction in Kerr-Schild coordinates  (2610.13684 - Wang et al., 9 Oct 2026) in Discussion, Section \ref{sec:summary}