to discuss exact black hole solutions for Lovelock gravity in the literature. The static, spherically symmetric black hole solutions in the theory have been found in [@Des; @Whee; @Cai1; @Cai4; @Banados; @CaiSoh; @Zaneli] and discussed [@Myers], and topological nontrivial black holes have been studied in [@Cai1; @Cai4; @CaiSoh; @Zaneli]. Some rotating solutions in Gauss-Bonnet theory have been studied in [@rotating; @Anabalon:2009kq]. However, a general rotating solution is still absent even in Gauss-Bonnet gravity. See also [@others; @others1] for some other extensions including perturbative AdS black hole solutions in the gravity theories with second order curvature corrections. For a nice review of black holes in Lovelock gravity, see [@GG].

Recently, Maeda and Dadhich presented a class of exact solutions in Gauss-Bonnet gravity [@Maeda:2006iw; @Maeda:2006hj; @Dadhich:2007xf; @Molina:2008kh] (Some similar black hole solutions have been found in Codimension-2 brane world theory [@CuadrosMelgar:2007jx; @CuadrosMelgar:2008kn]). They assumed the spacetime has a direct product structure (one is a four/three-dimensional spacetime, the other is a negative constant curvature space), and then split the equations of motion into two sets according to the direct product structure of spacetime. For a suitable choice of those coefficients in Gauss-Bonnet gravity so that the set of equations of motion for the 