Attractors and first order formalism in five dimensions revisited

TL;DR

This paper revisits the attractor mechanism in five-dimensional Einstein-Maxwell Chern-Simons theory, deriving a general fake superpotential and analyzing attractor flows for various charge configurations and geometries.

Contribution

It constructs a general fake superpotential expression in five dimensions applicable to all charge configurations and specific models, enhancing understanding of attractor flows.

Findings

Derived a universal fake superpotential for all charge setups.

Explicit solutions for $t^3$ and $stu$ models.

Analyzed attractor flows and horizon values of fields.

Abstract

The attractor mechanism in five dimensional Einstein-Maxwell Chern-Simons theory is studied. The expression of the five dimensional rotating black object potential depending on Taub-NUT, electric and magnetic charges as well as on all the scalar and gauge fields, is investigated. The first order formalism in d=5 is constructed and analyzed. We derive a general expression defining the fake superpotential which is valid for all charge configurations. An explicit expression for the fake superpotential is constructed, for all very special geometries, in the case of vanishing Taub-NUT charge. We carry out an analogous construction in the very special geometries corresponding to $t^3$ and $stu$ models, for the most general charge configurations. The attractor flows and horizon values of all fields are given.