Attractors in Black

TL;DR

This paper reviews recent advances in understanding the attractor geometries of extremal dyonic black holes in N=2 supergravity, classifying their charge orbits and scalar moduli spaces for symmetric special Kähler geometries and extended supergravities.

Contribution

It provides a comprehensive classification of attractor charge orbits and moduli spaces in N=2 and extended supergravities with symmetric special Kähler geometries.

Findings

Complete classification of charge orbits for symmetric geometries.

Identification of moduli spaces for non-BPS attractors.

Extension of classification to N>2 supergravities.

Abstract

We review recent results in the study of attractor horizon geometries (with non-vanishing Bekenstein-Hawking entropy) of dyonic extremal d=4 black holes in supergravity. We focus on N=2, d=4 ungauged supergravity coupled to a number n_{V} of Abelian vector multiplets, outlining the fundamentals of the special Kaehler geometry of the vector multiplets' scalar manifold (of complex dimension n_{V}), and studying the 1/2-BPS attractors, as well as the non-BPS (non-supersymmetric) ones with non-vanishing central charge. For symmetric special Kaehler geometries, we present the complete classification of the orbits in the symplectic representation of the classical U-duality group (spanned by the black hole charge configuration supporting the attractors), 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). Finally, we report on an analogous classification for N>2-extended, d=4 ungauged supergravities, in which also the 1/N-BPS attractors yield a related moduli space.