Small black holes in the large D limit

Abstract

The large D limit of AdS₂ × S ^D−2 solutions in the particular higher-derivative Lovelock-type theory is analyzed. The theory and the solutions were originally considered in an attempt to effectively describe near-horizon behavior of D-dimensional spherically symmetric 2-charge small extremal black holes which in superstring theory context are assumed to correspond to configurations in S ¹ × T ^9−D compactification schemes in which fundamental string is wound around circle S ¹. Though in D → ∞ limit the action contains infinite number of higher-derivative terms, their contributions to equations of motion sum into simple exponential form which allows us to find explicit solutions. A simplicity of this example gives us the opportunity to study some connections between α′ and 1/D expansions. In the leading order in 1/D the relation between the string parameter α′ and the radius of the horizon r _h (in the string frame) satisfies r _h ∝ $D\sqrt{{\alpha \prime }}$, i.e., we obtain an explicit realization of the relation inferred by Emparan et al. in the different context of large black holes in the ordinary Einstein gravity where α′ is not manifestly present.