Black objects in the Einstein-Gauss-Bonnet theory with negative cosmological constant and the boundary counterterm method

We propose to compute the action and global charges of the asymptotically anti-de Sitter solutions in Einstein-Gauss-Bonnet theory by adding boundary counterterms to the gravitational action. The general expression of the counterterms and the boundary stress tensor is presented for spacetimes of dimension $d\leq 9$. We apply this tehnique for several different types of black objects. Apart from static and rotating black holes, we consider also Einstein-Gauss-Bonnet black string solutions with negative cosmological constant.