Novel Geometrical Models of Relativistic Stars. I. The General Scheme

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 brings us to a two parameter family of relativistic stars without stiff functional dependence between the stelar radius and stelar mass. It turns out that within this family there do exist relativistic stars with arbitrary large mass, which are to have arbitrary small radius and arbitrary small luminosity. In addition, point particle idealization, as a limiting case of bodies with finite dimension, becomes possible in GR, much like in Newton gravity.