Does a black hole second law hold beyond effective field theory?
In plain words
In Einstein's theory a black hole's horizon area never decreases, which is why area acts as entropy. For theories with extra curvature terms a growing entropy is now proved when the extra terms are small corrections, but not when they are treated as exact.
Precise statement
Davies and Reall (2023) built a dynamical entropy, order by order in derivatives, that obeys a second law non-perturbatively in the perturbation amplitude for any gravitational effective field theory while the black hole stays within the effective-theory regime. Determine whether a second law holds for a higher-curvature theory taken as exact, such as Einstein-Gauss-Bonnet in $D > 4$ or a UV-complete string effective action, outside the effective-theory regime, and whether the dynamical entropy is unique up to stated ambiguities. An answer is a proof or an explicit violating solution.
What would settle it
A proof of a nonlinear second law for an exact higher-curvature theory outside the effective-theory regime, or an explicit violating solution.
Status in the literature
Unverified note
A non-perturbative second law in effective field theory at any fixed derivative order was proved by Davies and Reall (arXiv:2312.07659, 2023); the case beyond the effective-theory regime is open as of 2026.