It is cool to have a mental freakout, and sit and show that it is not a problem. I wondered if I had looked adequately at my fields, transformed into covariant vectors. I created them to satisfy zero divergence and THIS IS DEFINED ONLY ON CONTRAVARIANT VECTORS, turns out!!!
OK my radial field is,  in ‘contra’ form,  1/ [r^2 + cos^2(theta)][ 1 + k/r P(theta)]. I started freaking because the covariant form is:    1/(r^2 + 1) [1 + k/r P]. This form is quite calm as r goes to zero, yah?? HOWEVER THE COSINE GOES ALL THE WAY TO ZERO, so how about the contravariant form, doesn’t it blow up.? NO, I just misled you. we don’t have to look all way to r=0, not in my physics !!! We only look into r=k, where the [] term does strictly become ZERO, ahhhhhhhhhhh.  Peace restored.
We are talking about the Pita bread being a really very thin layer these days. If you consider the coordinate line segment between x=0 and x=1, the thickness described by the CLASSICAL ENERGY RADIUS, would be 1/137.  I DECLARE THIS APPROACH FOOLISH.  Who the hell cares about the CLASSICAL ENERGY RADIUS HERE??? CAN WE BLAME THE REPUBLICANS FOR  THIS MEASELY THIN LAYER OF BREAD ???
****Summary if you need one, lines exit the ellipse, yes, sort of, being  weak. They are ‘entirely’ radial here, which is to say, on the thetaclines, which as you now see, rapidly wrap… it is surely fun if you are watch my angle ‘b’ gyrate hereabouts… it has as numerator, r^2 + cos^2, and both are getting ‘small’, haaaaaaaaaaaa.


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