Logarithmic correction to the entropy of near-extremal higher-curvature black holes

The spherically symmetric sector of broad classes of $D$-dimensional gravitational theories can be effectively described by general two-dimensional Horndeski theories. Exploiting this correspondence, we study the low-temperature dynamics of near-extremal black hole solutions of the parent theories by deriving a universal near-horizon effective description in terms of Jackiw–Teitelboim (JT) gravity. We explicitly show that the logarithmic quantum correction to the entropy, $S_{\mathrm{J}\mathrm{T}}=\frac{3}{2}\log \left(T\mathrm{/}{T}_{\mathrm{b}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{k}\mathrm{d}\mathrm{o}\mathrm{w}\mathrm{n}}\right)$, previously derived for near-extremal black holes in Einstein gravity coupled to matter from the one-loop exact JT partition function, is universal across all models admitting an effective two-dimensional Horndeski description. We determine the general form of the scale at which this correction becomes dominant, $T_{\mathrm{b}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{k}\mathrm{d}\mathrm{o}\mathrm{w}\mathrm{n}}$, in terms of the data of the $D$-dimensional theories. We illustrate our general results with charged black holes in Lovelock gravities and regular black holes in Quasitopological gravities.