This paper suggests that the “spontaneous creation of matter in strong gravitation fields” – which is asserted in some papers – may be a result of an inconsistent approximation for the simultaneous systems of Einstein field equations and of matter field equations.

Firstly we shall remark that Einstein's dynamical equation is not only the consequence of the Einstein field equations (via Bianchi identity) but also the consequence of the relativistic matter field equations and of the weak principle of equivalence. Therefore, for all discussions we must start from the dynamical equation and from the conservation laws of charges.

Secondly, we find a formal inhomogeneous dynamical equation for the matter tensor by working in a background-field approximation. But, this inhomogenity vanishes according to the matter field equations.

Thirdly, we discuss the properties in an evolution-cosmos. In such cosmos a law of conformal conservation of energy is fulfilled. From this conservation law results that the energy is a continuous function of the gauge of time. Such continuous dependence involves the constance of discrete numbers according to the well known argument of Planck.