Exploring the relation between 4D and 5D BPS solutions

TL;DR

This paper establishes a detailed correspondence between four- and five-dimensional BPS solutions in N=2 supergravity, highlighting their common harmonic functions and attractor equations, with applications to black holes and rings in complex spacetimes.

Contribution

It provides the explicit dictionary linking 4D and 5D supersymmetric solutions, including generalizations with more complex prepotentials and their corrections.

Findings

Unified description of 4D and 5D BPS solutions using harmonic functions.

Explicit example with black holes and black rings in G"odel-Taub-NUT spacetime.

Discussion of corrections due to more general prepotentials.

Abstract

Based on recent proposals linking four and five-dimensional BPS solutions, we discuss the explicit dictionary between general stationary 4D and 5D supersymmetric solutions in N=2 supergravity theories with cubic prepotentials. All these solutions are completely determined in terms of the same set of harmonic functions and the same set of attractor equations. As an example, we discuss black holes and black rings in G\"odel-Taub-NUT spacetime. Then we consider corrections to the 4D solutions associated with more general prepotentials and comment on analogous corrections on the 5D side.