On Thursday, June 28, 2018 at 2:00:07 AM UTC-5, Jay R. Yablon wrote:   
   > I have now completed and submitted for peer review, the paper I   
   > previewed earlier here, which uses Dirac theory to ensure   
   > five-dimensional general covariance for the Kaluza-Klein metric   
   > tensor.  In this revision, there are several new sections including   
   > a detailed review of the Lorentz Force equation of motion for   
   > electrodynamics and some new insights about the Klauza-Klein scalar.   
      
   What are the monopole solutions?   
      
   More explicitly: find all the solutions that have the following symmetries:   
   * time-translation symmetry   
   * 2-sphere symmetry about a fixed center   
   but *not* necessarily symmetry with respect to the 5th coordinate nor   
   with g55 fixed to anything. Instead, pose the following condition:   
   * G_{mu nu} = 0, for all (mu,nu) possibly except (5,5).   
      
   Prove that the solutions separate into 2 families:   
   (A) a 2 parameter family in which g55 is constant but G_{55} is not 0   
   (B) a 3 parameter family in which G_{55} is 0, but g55 is not constant.   
   What's the 3rd parameter in (B)? (Hint, write down the effective em   
   force law for the monopole solution.)   
      
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