New anisotropic Gauss-Bonnet black holes in five dimensions at the critical point

We obtain new vacuum static black hole solutions with anisotropic horizons in Einstein-Gauss-Bonnet gravity with a negative cosmological constant in five dimensions. The translational invariance along one direction on the 3-dimensional horizon cross section is broken. The Gauss-Bonnet coupling alpha is at the critical point where there is one single AdS vacuum. These solutions does not appear in the form of a warped product, i.e. they lack a common warping factor, and the metric contains 2 arbitrary functions, h(r) of the radial coordinate r and H(y) of the horizon coordinate y - some degeneracy in the metric. The nontrivial horizon and the degeneracy may be closely related to the critical value of alpha. We introduce the process of obtaining the solutions and some of their properties, and also prove a uniqueness theorem for the case when there is a common warping factor for the rest two directions.