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16:08
Okay, I think I may have arrived at a description of my field that might lend itself to an equation. It's a hypersphere. Or the surface of a hypersphere, mapped onto more typical three dimensional space. One of the dimensions might be negative, though.
Which sounds like gibberish, granted. Two dimensional surface of an event horizon, mapped by a third closed dimension as distance. And hey, it's still a soliton, albeit a bizarre one.
I expect it to yield a curvature that is approximately sin(ln(x))/x, if my thinking is correct. Lost the divide-by-x^2 in favor of dividing by x when I switched to treating it as a two dimensional surface, instead of trying to force my intuitions of how it should behave using an assumption of flat space.
 
3 hours later…
18:46
Huh. It's a three-sphere with one point taken away. It's 3D space. Granted one of the dimensions might be negative. What the hell does that mean.

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