Solitonic generation of five-dimensional black ring solution

Abstract

Using the solitonic solution-generating technique we rederived the one-rotational five-dimensional black ring solution found by Emparan and Reall. The seed solution is not the Minkowski metric, which is the seed of $S^2$-rotating black ring. The obtained solution has more parameters than the Emparan and Reall's $S^1$-rotating black ring. We found the conditions of parameters to reduce the solution to the $S^1$-rotating black ring. In addition we examined the relation between the expressions of the metric in the prolate-spheroidal coordinates and in the canonical coordinates.

Figures (2)

• Figure 1: Schematic pictures of rod structures. The upper panel shows the rod structure of Minkowski spacetime, which is a seed of $S^2$-rotating black ring. The lower panel shows the rod structure of the $S^2$-rotating black ring. The segment $[-\sigma,\sigma]$ of semi-infinite rod in the upper panel is tranformed to the finite timelike rod with $\phi$-rotation by the solution-generating transformation. The eigenvector of the finite timelike rod in the lower panel has non-zero $\phi$ component. Therefore we put this rod between $x^0$ and $\phi$ axes.
• Figure 2: Schematic pictures of rod structures. The upper panel shows the rod structure of seed metric of $S^1$-rotating black ring. The lower panel shows the rod structure of $S^1$-rotating black ring. The finite spacelike rod $[-\eta_1\sigma,\eta_2\sigma]$ in the upper panel is altered to the finite timelike rod by the solution-generating transformation.