Entropy function for rotating extremal black holes in very special geometry

TL;DR

This work studies entropy of rotating extremal black holes in five-dimensional N=2 supergravity with cubic prepotentials by exploiting a five-to-four-dimensional connection via Taub-NUT geometry. The authors define a five-dimensional entropy function through dimensional reduction to the four-dimensional entropy function, carefully accounting for Chern-Simons contributions, and derive attractor equations for the near-horizon data. They construct and solve two distinct classes of solutions corresponding to different charge configurations (P^0,Q_A) and (P^0,Q0), obtaining explicit entropies and connecting them to angular momentum. The results clarify how five-dimensional rotating attractors relate to four-dimensional static or rotating attractors and outline extensions to include magnetic charges and more general rotations.

Abstract

We use the relation between extremal black hole solutions in five- and in four-dimensional N=2 supergravity theories with cubic prepotentials to define the entropy function for extremal black holes with one angular momentum in five dimensions. We construct two types of solutions to the associated attractor equations.