On R**2 Corrections for 5D Black Holes

TL;DR

The work analyzes supersymmetric R^2 corrections to extremal 5D black holes and strings in N=2 supergravity, employing a fully supersymmetric four-derivative action to build a generalized very special geometry. It develops a framework that uses c-extremization for black strings and the entropy function for black holes, producing corrected entropies that can be written in terms of shifted charges q^+_I and highlighting a six-dimensional bundle picture that connects near-horizon M2/M5 configurations under R^2 terms. A key result is that horizon entropy retains the same functional form as at tree level, with charges shifted by higher-derivative data, and that small black holes become regular with finite entropy; a Gauss–Bonnet comparison confirms consistency of the supersymmetric corrections. These findings illuminate the microstate structure of 5D BPS black holes in M-theory and provide a versatile method to include higher-derivative corrections in Calabi–Yau compactifications.

Abstract

We study higher order corrections to extremal black holes/black string in five dimensions. These higher order corrections are due to supersymmetric completion of R**2 term in five dimensions. By making use of the results we extend the notion of very special geometry when higher derivative terms are also taken into account. This can be used to make a connection between total bundle space of near horizon wrapped M2's and wrapped M5's in the presence of higher order corrections. We also show how the corrected geometry removes the singularity of a small black hole.