When does black hole entropy need a correction beyond the standard formula?

Black hole entropy is usually calculated using the Wald formula, but when matter fields behave badly at the horizon, that formula can miss finite contributions. This work provides a clean decomposition of the total entropy into three pieces — Wald entropy, a non-Wald Noether charge part, and a remaining integrable correction — and applies it to three concrete theories involving Kalb-Ramond, bumblebee, and Gauss-Bonnet fields. Depending on the theory, these correction terms can vanish, survive independently, or cancel each other, giving practitioners a direct diagnostic for when the standard Wald approach is actually enough.