All integrable 2D Horndeski theories (and thus many regular black-hole metrics) arise as spherical reductions of pure d≥4 gravities, which the paper terms quasi-topological.
Einstein-Gauss-Bonnet Gravity in Four-Dimensional Spacetime
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All $2D$ generalised dilaton theories from $d\geq 4$ gravities
All integrable 2D Horndeski theories (and thus many regular black-hole metrics) arise as spherical reductions of pure d≥4 gravities, which the paper terms quasi-topological.