{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"5f792a1d684afa6ca858c605e9f4999b3bd69458d98d1cf447bbdbcd4bc24e72","created":"2026-10-03T07:18:04Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"61c170e60d9dca0b7c8e70084a1d6ac282b54787af016d8a0ad6008bcc401ab2","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"grav.modified-gravity.second-law-higher-curvature","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"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.","posed_since":"","precise":"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.","problem_ref":null,"references":"","settled_by":"A proof of a nonlinear second law for an exact higher-curvature theory outside the effective-theory regime, or an explicit violating solution.","status_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.","title":"Does a black hole second law hold beyond effective field 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