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Scalar and gravitational horizon hair as observable imprints of extremal black hole spacetimes

Presenter
January 8, 2026
Abstract
The classical no-hair theorems assert that black holes are characterized by only a few parameters (mass, charge, spin), but recent work challenges this simplification — at least in the extremal limit. Recent theoretical investigations suggest a potential "loop hole" in the traditional no-hair theorem, revealing that certain conserved charges, known as horizon hair, can persist on their event horizons in the context of linearized perturbation theory. Our research focuses on providing strong numerical evidence for the external measurability of these charges. By analyzing the late-time asymptotic tail behavior of the radiation field at future null infinity, we derive and numerically analyse a characteristic expression to confirm that it is non-zero only in the extremal case (ERN and EK) and asymptotes to zero for subextremal cases. This finding establishes it as an observational signature for extremality. We then extend this concept to the more astrophysically relevant scenario of non-axisymmetric gravitational perturbations on extremal Kerr spacetime. We propose a non-axisymmetric gravitational charge based on the transverse derivative of the Beetle-Burko scalar on the horizon. Through numerical solutions of the Teukolsky equation, focusing on the dominant radiative quadrupolar (ℓ=m=2) mode, we show that the quantity is conserved on the horizon at late times. Crucially, we demonstrate a linear relationship between this conserved horizon charge and the associated Ori-coefficient that can be extracted from the black hole's exterior at a finite distance. This connection suggests that the non-axisymmetric gravitational hair is also potentially observable.
Supplementary Materials