Living on the Edge of Effective Field Theory: Near-Extremal Black Holes in Quadratic Gravity

Kelvin Ka-Ho Lam; Gary T. Horowitz; Nicolás Yunes

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arXiv · 2608.05268

Living on the Edge of Effective Field Theory: Near-Extremal Black Holes in Quadratic Gravity

Kelvin Ka-Ho Lam·Gary T. Horowitz·Nicolás Yunes

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Abstract

Near-extremal black holes can amplify higher-derivative corrections to general relativity, making them sharp probes of the perturbative control of gravitational effective field theory. We study this question in quadratic gravity with a dynamical scalar degree of freedom, focusing on dynamical Chern-Simons and scalar Gauss-Bonnet gravity. Using pseudospectral methods, we construct rapidly rotating exterior solutions at fixed surface gravity and fixed horizon angular velocity, and follow this controlled family toward extremality. In dynamical Chern-Simons gravity, the sequence approaches an asymptotically flat extremal exterior whose near-horizon limit agrees with the dynamical-Chern-Simons-deformed near-horizon extremal Kerr geometry and inherits its enhanced $SO(2,1)\times U(1)$ symmetry. In scalar Gauss-Bonnet gravity, the same limiting procedure behaves differently: the scalar develops an unavoidable logarithmic singularity at the horizon, the exterior metric develops a small boundary layer near the horizon, and the scalar-Gauss-Bonnet-deformed near-horizon extremal solution is not connected to a regular asymptotically flat exterior. We then use curvature invariants and tidal forces to diagnose the breakdown of the perturbative effective-field-theory expansion. We find that scalar curvature invariants can remain finite at the horizon even when tidal forces measured by infalling observers diverge as inverse powers of the surface gravity. These results separate distinct notions of effective-field-theory breakdown near extremality and provide a perturbative validity estimate that can be compared with current bounds on the dynamical Chern-Simons and scalar-Gauss-Bonnet couplings.

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Kelvin Ka-Ho Lam, Gary T. Horowitz, Nicolás Yunes. 2026-08-05. Living on the Edge of Effective Field Theory: Near-Extremal Black Holes in Quadratic Gravity. https://arxiv.org/abs/2608.05268

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