A black hole spun up almost to its limit is like an athlete balancing on the edge of a record. The most interesting action isn't inside the hole itself, but in the thinnest film of spacetime at its horizon. It's there that tiny corrections to Einstein's gravity can suddenly swell to gigantic proportions.
The authors of the study took two popular theories with such corrections: dynamical Chern-Simons and scalar Gauss-Bonnet. Using precise numerical methods, they constructed solutions for rapidly spinning black holes and carefully pushed them toward the limiting speed. In the first theory, everything went smoothly: they got a regular hole, and its immediate vicinity exactly matched the known symmetric solution. But in the second theory, catastrophe struck. The scalar field (a special characteristic of space) refused to be smooth and produced a logarithmic singularity at the horizon, as if space itself were tearing there.
This contrast is not just a mathematical curiosity. It separates two notions of "breaking down" in a theory. One thing is when spacetime curvature remains finite, and quite another when tidal forces become infinite. For Chern-Simons theory, the first sign stays silent, while the second screams trouble. For Gauss-Bonnet theory, the trouble is immediately visible. Such diagnostics provide a way to gauge how far calculations in these theories can be trusted, and to compare with existing constraints from observations.
as written by the authors arXiv:2608.05268v1
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.
The logarithmic singularity that emerged in Gauss-Bonnet theory is not just an abstraction. Similar logarithmic terms appear in quantum corrections to gravity, hinting at a deep connection between classical extensions of Einstein's theory and quantum effects.