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Among various strong-curvature extensions to General Relativity,Einstein-Dilaton-Gauss-Bonnet gravity stands out as the only nontrivial theorycontaining quadratic curvature corrections while being free from theOstrogradsky instability to any order in the coupling parameter. We derive anapproximate stationary and axisymmetric black-hole solution of thisgravitational theory in closed form, which is quadratic in the black-hole spinangular momentum and of seventh order in the coupling parameter of the theory.This extends previous work that obtained the corrections to the metric only atthe leading order in the coupling parameter, and allows us to consider valuesof the coupling parameter close to the maximum permitted by theoreticalconstraints. We compute some geometrical properties of this solution, such asthe dilaton charge, the moment of inertia and the quadrupole moment, and itsgeodesic structure, including the innermost-stable circular orbit and theepicyclic frequencies for massive particles. The latter represent a valuabletool to test General Relativity against strong-curvature corrections throughobservations of the electromagnetic spectrum of accreting black holes.

Rotating black holes in Einstein-Dilaton-Gauss-Bonnet gravity with finite coupling