Solitonic generation of vacuum solutions in five-dimensional General Relativity

Abstract

We describe a solitonic solution-generating technique for the five-dimensional General Relativity. Reducing the five-dimensional problem to the four-dimensional one, we can systematically obtain single-rotational axially symmetric vacuum solutions. Applying the technique for a simple seed solution, we have previously obtained the series of stationary solutions which includes $S^2$-rotating black ring. We analyze the qualitative features of these solutions, e.g., conical singularities, closed timelike curves, and spacetime curvatures. We investigate the rod structures of seed and solitonic solutions. We examine the relation between the expressions of the metric in the prolate-spheroidal coordinates and in the C-metric coordinates.

18 pages, 10 figures, published version

References in corpus (4)

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

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• Binary Darboux Transformations in Bidifferential Calculus and Integrable Reductions of Vacuum Einstein Equations
• Myers-Perry Black Hole in an External Gravitational Field
• Doubly Spinning Black Rings
• Thermodynamic black di-rings
• Generating Generalized $G_{D-2}$ solutions