A new interior Schwarzschild solution

Abstract A new interior Schwarzschild solution is presented. It is static, spherically symmetric, regular everywhere inside a sphere of coordinate radius a, and across the surface of this sphere it is joined smoothly to the exterior Schwarzschild solution. There are no radial stresses inside the sphere. The radius a is subject to the inequality a 2m, where m is the gravitational mass of the sphere. Under certain conditions the new solution may be interpreted as the field inside an Einstein cluster.