Black Holes and Attractors in Supergravity

TL;DR

This paper explores the properties of extremal black holes in four-dimensional supergravity, emphasizing the attractor mechanism, the role of superpotentials, and the influence of U-duality in classifying black hole solutions.

Contribution

It demonstrates that non-supersymmetric extremal black holes can be described by first order flow equations using a superpotential, and reviews the role of U-duality in supergravity black hole classification.

Findings

Regular solutions exhibit attractor behavior for scalar fields.

Black holes can be characterized by a superpotential W.

U-duality helps classify black hole solutions and determine their properties.

Abstract

We discuss some of the basic features of extremal black holes in four-dimensional extended supergravities. Firstly, all regular solutions display an attractor behavior for the scalar field evolution towards the black hole horizon. Secondly, they can be obtained by solving first order flow equations even when they are not supersymmetric, provided one identifies a suitable superpotential W which also gives the black hole entropy at the horizon and its ADM mass at spatial infinity. We focus on N=8 supergravity and we review the basic role played by U-duality of the underlying supergravity in determining the attractors, their entropies, their masses and in classifying both regular and singular extremal black holes.