The Black Di-Ring: An Inverse Scattering Construction

TL;DR

This work addresses constructing concentric non-supersymmetric black rings in five dimensions using the inverse scattering method (ISM). Starting from a Harmark rod seed, the authors apply a two-soliton Belinski–Zakharov dressing to generate a concentric black di-ring, then enforce asymptotic flatness and remove conical singularities, leaving three physical moduli and explicit expressions for the ADM mass and angular momentum: $M_{ADM}=rac{3\pi}{4}(a_6-a_4+a_3-a_1)$ and $J_{ADM}=\pi \frac{(a_2-a_1)(a_5-a_1)c_1+(a_4-a_2)(a_5-a_4)c_2}{2(a_4-a_1)}$. The construction demonstrates a genuinely five-dimensional route to multi-ring solutions, enabling generalizations to more intricate axially symmetric configurations and analysis of their thermodynamics and phase structure, including potential equilibrium between the rings. The results also connect to the known single-ring limit and provide a framework for exploring non-uniqueness of higher-dimensional black holes. Overall, the paper establishes a robust ISM-based derivation of concentric black di-rings and opens avenues for detailed phenomenology in higher-dimensional gravity.

Abstract

We use the inverse scattering method (ISM) to derive concentric non-supersymmetric black rings. The approach used here is fully five-dimensional, and has the modest advantage that it generalizes readily to the construction of more general axi-symmetric solutions.

Figures (2)

• Figure 1: Rod configuration for the seed solution
• Figure 2: Rod configuration for the final solution.