Vaccum solutions of five-dimensional Einstein equations generated by inverse scattering method II : Production of black ring solution

Abstract

We study vacuum solutions of five-dimensional Einstein equations generated by the inverse scattering method. We reproduce the black ring solution which was found by Emparan and Reall by taking the Euclidean Levi-Civita metric plus one-dimensional flat space as a seed. This transformation consists of two successive processes; the first step is to perform the three-solitonic transformation of the Euclidean Levi-Civita metric with one-dimensional flat space as a seed. The resulting metric is the Euclidean C-metric with extra one-dimensional flat space. The second is to perform the two-solitonic transformation by taking it as a new seed. Our result may serve as a stepping stone to find new exact solutions in higher dimensions.

12 pages, to be published in PRD

References in corpus (2)

• Complete integrability of higher-dimensional Einstein equations with additional symmetry, and rotating black holes
• Completely integrable sector in 5D Einstein-Maxwell gravity and derivation of the dipole black ring solutions

Cited by in corpus (12)

• Boundary Value Problem for Black Rings
• 5D Einstein-Maxwell solitons and concentric rotating dipole black rings
• Solitonic generation of vacuum solutions in five-dimensional General Relativity
• Relationship Between Solitonic Solutions of Five-Dimensional Einstein Equations
• Rotating Black Holes on Kaluza-Klein Bubbles
• Generating technique for $U(1{)}^{3}5D$ supergravity
• Supersymmetric Black Rings on Eguchi-Hanson Space
• On Black Ring with a Positive Cosmological Constant
• Multi-Black Rings on Eguchi-Hanson Space
• Rotating dyonic dipole black rings: exact solutions and thermodynamics
• Doubly Spinning Black Rings
• Generating Generalized $G_{D-2}$ solutions