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We construct an analytical approximation for the numerical black hole metricof P. Kanti, et. al. [PRD54, 5049 (1996)] in the four-dimensionalEinstein-dilaton-Gauss-Bonnet (EdGB) theory. The continued fraction expansionin terms of a compactified radial coordinate, used here, converges slowly whenthe dilaton coupling approaches its extremal values, but for a black hole farfrom the extremal state, the analytical formula has a maximal relative error ofa fraction of one percent already within the third order of the continuedfraction expansion. The suggested analytical representation of the numericalblack hole metric is relatively compact and good approximation in the wholespace outside the black hole event horizon. Therefore, it can serve in the sameway as an exact solution when analyzing particles' motion, perturbations,quasinormal modes, Hawking radiation, accreting disks and many other problemsin the vicinity of a black hole. In addition, we construct the approximateanalytical expression for the dilaton field.

An analytical approximation for the Einstein-dilaton-Gauss-Bonnet black hole metric