A class of static, axisymmetric, interior solutions of Einstein's field equations in general relativity is obtained. The solutions are physically reasonable, and can be interpreted as sources for Weyl and Levi-Civita's general exterior solution that is flat at infinity, by making the metric components and their derivatives continuous at the boundary of the matter. For a particular model, a correlation is exhibited between the structure of the source material and the exterior field, which resembles closely, but not exactly, that of the corresponding Newtonian model.

• Received 9 June 1967

DOI:https://doi.org/10.1103/PhysRev.163.1373