Corrections to macroscopic supersymmetric black-hole entropy

TL;DR

This paper calculates the corrections to the entropy of extremal black holes in N=2, D=4 supergravity, incorporating quadratic Riemann tensor terms, and confirms agreement with microstate counting in string theory.

Contribution

It derives a modified entropy formula for extremal black holes that accounts for quadratic curvature corrections and aligns with string microstate counts.

Findings

The corrected entropy depends only on electric/magnetic charges.

The new entropy formula is expressed via a single holomorphic function.

Results are consistent with previous microstate counting in string theory.

Abstract

We determine the corrections to the entropy of extremal black holes arising from terms quadratic in the Riemann tensor in $N=2, D=4$ supergravity theories. We follow Wald's proposal to modify the Bekenstein-Hawking area law. The new entropy formula, whose value only depends on the electric/magnetic charges, is expressed in terms of a single holomorphic function and is consistent with electric-magnetic duality. For string effective field theories arising from Calabi-Yau compactifications, our result for the entropy of a certain class of extremal black-hole solutions fully agrees with the counting of microstates performed some time ago by Maldacena, Strominger, Witten and by Vafa.