# Vortex ring solutions in General Relativity

Vortex rings are captivating toroidal self-reinforcing fluid systems that can happen in turbulent fluids. I wonder if something similar can exist as a solution to Einstein's gravitational equations

• It is a bit tricky to see what would be the analogy here. Torus-shaped spacetimes are possible, but there nothing is moving. A heavy vortex ring in a fluid would of course have some self gravity. But gravity waves with enough energy to bend their propagation into something vortexlike sounds very hard to analyse. – Anders Sandberg Dec 12 '18 at 14:02
• @AndersSandberg could perhaps a "closed ring chain" of Kerr black holes rotating in the same direction do the trick? In a torus there are two rotation symmetries, if the ring of black holes is stable or metastable (say, they rotate around the common center at the right angular speed) composed with their intrinsic Kerr rotation, looks to me that such an spacetime would look very close to this – lurscher Dec 12 '18 at 15:29
• There are black rings solutions in 5D general relativity with horizon topology of $S_2\times S_1$ but rotation is (4D) toroidal rather than poloidal. – A.V.S. Dec 12 '18 at 16:06
• I like the idea of a ring of Kerr black holes, it comes close to the vortex ring. But the topology censorship theorem seems to rule out merging them into a black vortex - they would just merge into a really wobbly big black hole if pushed too close. – Anders Sandberg Dec 12 '18 at 18:52
• "Vortex rings are captivating toroidal self-reinforcing fluid systems that can happen in turbulent fluids." Why do you specify turbulent fluids? Can't they also form in laminar flows? – D. Halsey Dec 12 '18 at 21:53