Underlying symmetry or deeper explanation of extremal RN dynamical Love-number properties

Determine whether the vanishing of the leading dynamical running of axial Love numbers for extremal ReissnerNordstr00om black holes is explained by a symmetry analogous to the ladder symmetries of static Love numbers or by another fundamental property of extremal black holes.

Background

The paper proves that the leading dynamical running of axial electromagnetic and gravitational Love numbers vanishes for extremal ReissnerNordstr00om black holes at every multipole. It attributes the result provisionally to the residue formula and the vanishing of the static tidal field on the degenerate horizon, but leaves unresolved whether a deeper symmetry or structural principle is responsible.

References

Its mechanism appears to be transparent enough through our residue formula and the fact that the static tidal field vanishes on the degenerate horizon, yet it is natural to ask whether this might be related to a symmetry, in the spirit of the ladder symmetries for static Love numbers (which is hinted at by our results for the anomalous dimension coefficients), or to some deeper property of extremal black holes.

— The Love for Three Logarithms: Universal Running of Dynamical Love Numbers  (2610.01152 - Garcia-Saenz, 1 Oct 2026) in Section 6, final paragraph