Abstract

An “analytic gravitational field”Z αβ(Z y ) is shown to include electromagnetic phenomena. In an almost flat and almost static complex geometryds 2 =zαβdzαdzβ of four complex variables zγ=t, x, y, x the field equationsR αβ $\frac{1}{2}$ Rz αβ= −κ(σU α U β − υZ αβ) imply the conventional equations of motion and the conventional electromagnetic field equations to first order if σ=σ(Z v) and ν=ν(z γ) are expressed in terms of the conventional mass density function $\hat \sigma = \hat \sigma (x^\gamma )$ , the conventional charge density function $\hat \varepsilon = \hat \varepsilon (x^\gamma )$ , and a pressurep as follows: $\sigma = - 2v - 2iv\hat \varepsilon /\hat \sigma ,v = v + i(\frac{1}{4}\hat \varepsilon + v\hat \varepsilon /\hat \sigma ),$ v=const=p/c 2≈−10−29 gm/cm3