A New Interior Schwarzschild Solution on the Gravitational Field of a Sphere of Compressible Fluid in General Relativity

A new interior Schwarzschild solution is presented. It is static, spherically symmetric, regular everywhere inside a sphere of radius r 1, 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 r 1 is subject to the inequality r 1>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.