The Uniform Transparent Gravitational Lens

TLDR: In this paper, an elementary discussion is given of the gravitational deflection of light due to radially and cylindrically symmetric masses and the effect of the deflection on apparent luminosity of distant sources is also considered.

Abstract: An elementary discussion is given of the gravitational deflection of light due to radially and cylindrically symmetric masses. The effect of the deflection on apparent luminosity of distant sources is also considered. All results are limited to weak, static, asymptotically flat gravitational fields. Emphasis here is on observations of sources aligned behind the disc of the deflecting mass so that the possible transparency of this mass is decisive in image formation. Detailed calculations are made for the simple case of the uniformly dense transparent sphere and comparisons are made with the opaque mass sphere. If they have the same mass and radius, the maximum light deflection produced by these lenses is nearly equal. However, their effects on the area of narrow light beams may be quite different. The uniform transparent sphere does not produce multiple images of one source and, to first order, introduces no image distortion.