  In a series of articles we describe a novel class of geometrical models of
relativistic stars. Our approach to the static spherically symmetric solutions
of Einstein equations is based on a careful physical analysis of radial gauge
conditions.
  It turns out that there exist heavy black dwarfs: relativistic stars with
arbitrary large mass, which are to have arbitrary small radius and arbitrary
small luminosity. In the present article we mathematically prove this new
phenomena, using a detailed consideration of incompressible GR stars. We study
the whole two parameter family of solutions of extended TOV equations for
incompressible stars. This example is used to illustrate most of the basic
features of the new geometrical models of relativistic stars. Comparison with
newest observational data is discussed
