electromagnetism - Do two bodies spinning about the same axis in the opposite direction repel each other?

I recently read about the GEM equations, which look very much like the Maxwell's equations.

Does this mean the behavior of mass is like the the behavior of the electric charge?

So for example if you spin a ring so you have ring "mass-current" do you get a "gravitomagnet"? If you get two of such spinning rings can you make them repel each other, like electromagnets do when the currect is opposite?