The vacuum field of the point-mass is an unrealistic idealization which does not occur in Nature - Nature does not make material points. A more realistic model must therefore encompass the extended nature of a real object. This problem has also been solved for a particular case by K. Schwarzschild in his neglected paper on the gravitational field of a sphere of incompressible fluid. I revive Schwarzschild's solution and generalise it. The black hole is necessarily precluded. A body cannot undergo gravitational collapse to a material point.