The Vanishing of the Non-linear Static Love Number of Kerr Black Holes and the Role of Symmetries

TL;DR

This paper demonstrates that Kerr black holes have zero static tidal Love numbers at all orders, revealing a deep connection between their tidal response and underlying non-linear symmetries, thus confirming their robustness against external tidal forces.

Contribution

It extends previous results for Schwarzschild black holes to Kerr black holes, showing their tidal Love numbers vanish at all orders due to non-linear symmetries.

Findings

Kerr black holes have zero static tidal Love numbers at all orders.

The vanishing is linked to non-linear symmetries of the spacetime.

Results generalize previous Schwarzschild black hole findings.

Abstract

We investigate the tidal response of Kerr black holes in four-dimensional space-times subjected to external gravitational fields. Using the Ernst formalism and Weyl coordinates, we analyze the non-linear tidal deformation of rotating black holes and demonstrate that their static tidal Love numbers vanish at all orders of the external tidal field. We also show that this result is intimately related to the presence of underlying non-linear symmetries. Our analysis generalizes previous findings for Schwarzschild black holes and confirms the robustness of four-dimensional black holes against tidal forces.