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Note on the form of the metric for an isolated vortex in general relativity. (English) Zbl 0757.76079

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
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