First-order attractor flow equations for supersymmetric black rings in N=2, D=5 supergravity

TL;DR

This paper derives and analyzes first-order attractor flow equations for supersymmetric and non-supersymmetric black rings in five-dimensional supergravity, providing new insights into their structure and solutions.

Contribution

It introduces the first-order flow equations for black rings in 5D supergravity, including both BPS and non-BPS cases, using very special geometry.

Findings

Derived general attractor flow equations for black rings

Solved flow equations and analyzed solution properties

Extended attractor mechanism to non-BPS black rings

Abstract

In this paper we investigate the attractor mechanism in the five dimensional low energy supergravity theory corresponding to M-theory compactified on a Calabi-Yau threefold $CY_3$. Using very special geometry, we derive the general first-order attractor flow equations for BPS and non-BPS solutions in five-dimensional Gibbons-Hawking spaces. Especially, considering the supersymmetric solution, we obtain the first-order flow equations for supersymmetric (multi)black rings. We also solve the flow equations and discuss some properties of the solutions of flow equations.