The principle of equivalence in the theory of variable rest mass with applications for astrophysics

The derivation of the covariant equation of a point of variable rest mass with regard to the dark energy on the basis of the principle of equivalence is considered in the article. As in GTR there is no formulations of of energy-momentum conservation for variable mass, the law of energy-momentum conservation for variable rest mass in STR studied by the author is used. For this purpose, a conversion of Kristoffel brackets and locally - Lorentz coordinates satisfying them are introduced. As a result it is possible to write in the small neighborhood the covariant equations of a point of variable rest mass in Riemannian space- time (Shvartsshild, Kerr) with continuous acceleration. In the article for the first time the dependence of the mass drop rate on the ratio of the current mass to the initial mass is also considered. The results could be used for investigation the process of falling of a point of variable mass on a black hole and to record the Kruskala coordinates.

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