Obstruction to local entropy laws on arbitrary black-hole cuts in five-dimensional Einstein–Gauss–Bonnet gravity

We study local entropy laws on arbitrary cuts of event horizons in five-dimensional Einstein–Gauss–Bonnet gravity, treated as an exact theory. No covariant local entropy can both reproduce the stationary black-hole entropy and be nondecreasing between every ordered pair of cuts, provided its density is smooth on an invariant open set of off-shell metric and cut jets containing a flat planar cut and every cut used in the argument. No global bound on derivative order is assumed. The counterexamples to the second law are vacuum black holes perturbed by a gravitational wave, with a strongly hyperbolic formulation near the relevant horizon interval and its stationary future. Shear makes the intrinsic curvature of a cut depend on its bending. The stationary entropy fixes the coefficient of this curvature term, and local corrections cannot cancel its response to cut bending. The obstruction appears at second order in wave amplitude on a smooth horizon, without a merger or topology change.