Observable consequences of higher-derivative–induced extremal divergences

Determine the observable consequences of the divergences (such as horizon tidal-force blow-ups and related divergences in background solutions and perturbations) that arise for extremal black holes when higher-derivative corrections to the Einstein–Hilbert action are included and the black hole is perturbed, specifically characterizing how the unbounded growth of these corrections as extremality is approached manifests in measurable observables for near-extremal rotating black holes.

Background

Recent work has shown that higher-derivative corrections to general relativity can produce divergences at extremality, including tidal-force blow-ups on horizons for perturbed black holes and even singular stationary solutions in certain beyond-GR theories. Although these divergences disappear in the near-extremal regime, the associated corrections grow without bound as extremality is approached.

The paper motivates a need to connect these theoretical divergences to concrete observables, noting that current understanding does not yet translate these findings into measurable predictions. This open problem seeks to bridge that gap by establishing how such divergences affect quantities accessible to observation, especially in systems relevant to gravitational-wave astronomy.