A FINITE INCOMPRESSIBLE MASS SHELL AS A SOURCE OF SCHWARZSCHILD SPACETIME

We analyse a solution of Einstein field equations which describe a fin ite incompressible and static spherical shell of matter as a source of the vacuum Schwarzschild spacetime. The outer boundary is at a coordi nate radius less than 9M/4 but the inner surface is singular as a cons equence of the assumed uniformity of the matter density. The presence of a curvature singularity at the inner surface allows the outer bound ary of the shell to be arbitrarily close to the Schwarzschild event ho rizon. Since the spacetime of the shell interior satisfies the conditi ons for the Lynden-Bell and Katz definition of matter and gravitationa l energies, we analyse how these quantities behave in the limit to a b lack hole.