Abstract
We find that anti--de Sitter (AdS) spacetime with a nontrivial linear dilaton field is an exact solution in the effective action of the string theory, which is described by gravity with the Gauss-Bonnet curvature terms coupled to a dilaton field in the string frame without a cosmological constant. The AdS radius is determined by the spacetime dimensions and the coupling constants of curvature corrections. We also construct the asymptotically AdS black hole solutions with a linear dilaton field numerically. We find these AdS black holes for hyperbolic topology and in dimensions higher than four. We discuss the thermodynamical properties of those solutions. Extending the model to the case with the even-order higher Lovelock curvature terms, we also find the exact AdS spacetime with a nontrivial dilaton. We further find a cosmological solution with a bounce of three-dimensional space and a solitonic solution with a nontrivial dilaton field, which is regular everywhere and approaches an asymptotically AdS spacetime.
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