Scalar Debye Potentials for Electromagnetic Fields in Spherical Gravity and Spherical Media. I

Modified scalar Debye potentials for electromagnetic (EM) waves in spherical gravity and spherical media are found. These potentials decompose the EM waves into two completely independent electric and magnetic radial modes and achieve scalarization and boundary fitting. Their equations, being different in a vacuum medium from ${{\Phi }^{;\mu }}_{;\mu }=0\mathrm{}$ of a scalar field, are reduced to one-dimensional Helmholtz equations under a separability condition, and can have their gravity effect "nullified" by a particular medium. Also the reflection coefficient $R_l$ for an $l$ spherical wave satisfies a Ricatti equation, and the phase shifts ${\delta }_l$ and scattering cross sections are related to $R_l$. For an incident plane EM wave, the nonforward differential scattering cross section is expressed in terms of the $R_l$ for the case where the medium and/or gravity tapers off slower than ${\mathrm{}\left(\mathrm{radius}\right)\mathrm{}}^{-1\mathrm{}}$ and $R_l$, ${\delta }_l$ themselves diverge.