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A "Smoke Ring" solution to EFEs?

  1. Dec 27, 2016 #1
    Hello, does anyone know if a solution to EFEs (Einstein's Field Equations) has been found that's analogous to Helmholtz's vortex ring solutions in fluid dynamics?
  2. jcsd
  3. Dec 28, 2016 #2

    Ben Niehoff

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    Are you specifically interested in black hole solutions? Or just generic, smooth solutions with some matter distribution (i.e., a fluid with a vortex ring, for example)?

    As far as black holes are concerned, in 5 dimensions, Emparan and Reall have written down a "black ring" solution with horizon topology ##S^1 \times S^2##. It has been expanded upon by others to include all sorts of angular momenta and charges.

    However, in 4 dimensions, stationary black holes must have spherical topology. Therefore if any sort of toroidal black hole exists, it must be non-stationary; i.e. time-dependent. It would quickly collapse into a standard Kerr black hole.
  4. Dec 28, 2016 #3
    Thanks Ben, just generic, smooth solutions with some matter distribution.
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