SAM Lectures on Extremal Black Holes in d=4 Extended Supergravity

TL;DR

This paper reviews recent classifications of extremal black hole attractors in N=2, d=4 supergravity, detailing charge orbit types, entropy, and moduli spaces, with extensions to higher N supergravities.

Contribution

It provides a comprehensive classification of charge orbits and moduli spaces for extremal black holes in N=2 and extended supergravities, including non-BPS solutions.

Findings

Classification of three classes of attractor solutions with non-zero entropy.

Identification of distinct charge orbit types and their properties.

Analysis of moduli spaces associated with non-BPS attractors.

Abstract

We report on recent results in the study of extremal black hole attractors in N=2, d=4 ungauged Maxwell-Einstein supergravities. For homogeneous symmetric scalar manifolds, the three general classes of attractor solutions with non-vanishing Bekenstein-Hawking entropy are discussed. They correspond to three (inequivalent) classes of orbits of the charge vector, which sits in the relevant symplectic representation R_{V} of the U-duality group. Other than the 1/2-BPS one, there are two other distinct non-BPS classes of charge orbits, one of which has vanishing central charge. The complete classification of the U-duality orbits, as well as of the moduli spaces of non-BPS attractors (spanned by the scalars which are not stabilized at the black hole event horizon), is also reviewed. Finally, we consider the analogous classification for N>2-extended, d=4 ungauged supergravities, in which also the 1/N-BPS attractors yield a related moduli space.