Black Holes in the Dilatonic Einstein-Gauss-Bonnet Theory in Various Dimensions. III - Asymptotically AdS Black Holes with k = +/- 1

We study black hole solutions in the Einstein-Gauss-Bonnet gravity with the dilaton and a negative cosmological constant. We derive the field equations for the static spherically symmetric (k = 1) and hyperbolically symmetric (k = -1) spacetime in general D dimensions. The system has some scaling symmetries which are used in our analysis of the solutions. Nontrivial asymptotically AdS solutions are obtained numerically, in D = 4 - 6 and 10 dimensional spacetimes. For spherically symmetric solutions, there is the minimum horizon radius below which no solution exists in D = 4 - 6. However in D = 10, there is not such lower bound but the solution continues to exist; to zero horizon size. For hyperbolically symmetric solution, there is the minimum horizon radius in all dimensions. Our solutions can be used for investigations of the boundary theory through AdS/CFT correspondence. We also discuss the possible fate of these black hole solutions.