Macroscopic Entropy of $N=2$ Extremal Black Holes

TL;DR

This paper derives a universal formula for the entropy of extremal BPS black holes in N=2 supergravity, showing that the horizon moduli are fixed by charges and independent of asymptotic conditions.

Contribution

It extends previous work by providing a universal entropy formula for dyonic extremal black holes, including both electric and magnetic charges.

Findings

Horizon moduli are fixed by charges and independent of asymptotic values.

A universal Bekenstein-Hawking entropy formula is derived.

The results generalize previous magnetic-only cases.

Abstract

Extremal BPS-saturated black holes in $N=2$, $d=4$ supergravity can carry electric and magnetic charges $(q^\Lambda_{(m)},q_\Lambda^{(e)})$. It is shown that in smooth cases the moduli fields at the horizon take a fixed "rational" value $X^\Lambda(q_{(m)},q^{(e)})$ which is determined by the charges and is independent of the asymptotic values of the moduli fields. A universal formula for the Bekenstein-Hawking entropy is derived in terms of the charges and the moduli space geometry at $X^\Lambda(q_{(m)},q^{(e)})$. This work extends previous results of Ferrara, Kallosh and the author for the pure magnetic case.