Some properties of an “aesthetic” field theory

We continue our study of the Lorentz-invariant field theory based on the equations _jk;l ⁱ =0 and g_ij;k=0. To first order in a perturbation expansion, we find _jk;l ⁱ =0 reduces to the wave equation. In orders higher than the first, we find that _jk;l ⁱ =0 cannot be linearized. We also find that the simple wave-type equation g^ij2g/xⁱx^j=0 is contained in the theory when an appropriate choice is made for the parameters at the origin point.