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We obtain new vacuum static black hole solutions with anisotropic horizons inEinstein-Gauss-Bonnet gravity with a negative cosmological constant in fivedimensions. The translational invariance along one direction on the3-dimensional horizon cross section is broken. The Gauss-Bonnet coupling{\alpha} is at the critical point where there is one single AdS vacuum. Thesesolutions does not appear in the form of a warped product, i.e. they lack acommon warping factor, and the metric contains 2 arbitrary functions, h(r) ofthe radial coordinate r and H(y) of the horizon coordinate y -- some degeneracyin the metric. The nontrivial horizon and the degeneracy may be closely relatedto the critical value of {\alpha}. We introduce the process of obtaining thesolutions and some of their properties, and also prove a uniqueness theorem forthe case when there is a common warping factor for the rest two directions.

New Anisotropic Gauss-Bonnet Black Holes in Five Dimensions at the Critical Point