Just as a reference I have found a PDF of a 1939 paper by Einstein online.

http://www.cscamm.umd.edu/tiglio/GR2012/Syllabus_files/EinsteinSchwarzschild.pdfOf particular interest is the statement on page numbered 928.

"Equation (14) represents a complicated relation between the particle density

n and the function a representing the gravitational field. The limiting case,

however, in which the gravitating particles are concentrated within an infinitely

thin spherical shell, between r = ro- A and r = ro, is comparatively simple.

Of course, this case could only be realized if the individual particles had the

rest-volume zero, which cannot be the case. This idealization, however, still is

of interest as a limiting case for the radial distribution of the particles"