Problems connected with the tangential metric coefficient in the Schwarzschild metric: A possible solution

Four situations are shown where the Schwarzschild metric cannot be used or is subject to unsurmountable problems. The first is the question of a metric useful for PPN-formalism checking different gravitational theories. The second problem occurs in connection with Mach's principle, when the flatness of the spacetime inside a massive hollow sphere is a generally accepted solution. The metrical discontinuity on the same spherical shell is a third problem. The fourth one is the anisotropy of the mass-energy of a test particle in the gravitational field. Three principles for solution are proposed:

1. The space is not dilated, but rather contracted, in the gravitational field; then the measurement-rods are shorter and measured distances have greater magnitudes.
2. The potential energy is to be related to a potential level where a stationary observer is placed and the general relativistic potential must be used.
3. A new metric must be introduced which is distinct from the Schwarzschild metric, so that the space in the gravitational field is warped isotropically.

Then the problems stated are shown to be easily solvable.