Supersymmetric Black Holes and Freudenthal Duality

TL;DR

This paper investigates how Freudenthal duality influences supersymmetric extremal black hole attractors in N=2, D=4 supergravity, revealing invariance of entropy and critical points, and exploring its effects on different black hole charge phases.

Contribution

It demonstrates that Freudenthal duality acts as an anti-involution on black hole charges, preserving entropy and critical points, and maps between different black hole charge configurations.

Findings

Freudenthal duality preserves black hole entropy.

It maps supersymmetric black holes to other solutions with different charge configurations.

Charge space contains mutually exclusive domains related by Freudenthal duality.

Abstract

We study the effect of Freudenthal duality on supersymmetric extremal black hole attractors in N = 2, D = 4 ungauged supergravity. Freudenthal duality acts on the dyonic black hole charges as an anti-involution which keeps the black hole entropy and the critical points of the effective black hole potential invariant. We analyze its effect on the recently discovered distinct, mutually exclusive phases of axionic supersymmetric black holes, related to the existence of non-trivial involutory constant matrices. In particular, we consider a supersymmetric D0-D4-D6 black hole and we explicitly Freudenthal-map it to a supersymmetric D0-D2-D4-D6 black hole. We thus show that the charge representation space of a supersymmetric D0-D2-D4-D6 black hole also contains mutually exclusive domains.