Higher-Order Black-Hole Solutions in N=2 Supergravity and Calabi-Yau   String Backgrounds
  Based on special geometry, we consider corrections to N=2 extremal black-hole solutions and their entropies originating from higher-order derivative terms in N=2 supergravity. These corrections are described by a holomorphic function, and the higher-order black-hole solutions can be expressed in terms of symplectic Sp(2$n$+2) vectors. We apply the formalism to N=2 type-IIA Calabi-Yau string compactifications and compare our results to recent related results in the literature. 
Klaus Behrndt, Gabriel Lopes Cardoso, Bernard de Wit, Dieter L\"ust,   Thomas Mohaupt and Wafic A. Sabra