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Description
Recent work has revealed that extremal Kerr black holes may exhibit a sensitivity to higher-derivative corrections to Einstein's equations, displaying singularities in the tidal forces at the horizon. However, in a purely gravitational context, this "ultraviolet sensitivity" translates into a strong dependence on the Wilson coefficients in the low-energy effective field theory. These, in turn, are fixed by the underlying theory of quantum gravity in the ultraviolet. I will discuss how these coefficients are predicted within the framework of asymptotically safe quantum gravity, and show that, if the quantum-gravity scale is trans-Planckian, this horizon-scale ultraviolet sensitivity is avoided. I will then discuss broader implications for the role of scales in asymptotically safe gravity coupled to matter, starting from the asymptotically safe postdiction of the top-quark mass and exploring the interplay between different notions of scales