Pekeris, C. L.; Frankowski, K. Note on the form of the metric for an isolated vortex in general relativity. (English) Zbl 0757.76079 Proc. Natl. Acad. Sci. USA 89, No. 15, 6703-6705 (1992). Summary: Calling a metric semidiagonal if it has a single off-diagonal element \(g_{\varphi t}\), we show that the stationary interior solution for a cylindrically symmetrical perfect fluid possessing an angular momentum cannot have a semidiagonal metric, unless the motion of the fluid particles is purely rotational around the axis of symmetry. A discussion is given of the relativistic spherical vortex in flat space, with a view of seeking a solution for such an isolated vortex in which gravitation is not neglected. MSC: 76Y05 Quantum hydrodynamics and relativistic hydrodynamics 53B50 Applications of local differential geometry to the sciences Keywords:cylindrically symmetrical perfect fluid; semidiagonal metric; spherical vortex PDFBibTeX XMLCite \textit{C. L. Pekeris} and \textit{K. Frankowski}, Proc. Natl. Acad. Sci. USA 89, No. 15, 6703--6705 (1992; Zbl 0757.76079) Full Text: DOI