On the definition of the vacuum in the Gravitational field; the $\Re$ vacuum

A new approach to definition of a vacuum in the external gravitational field is suggested, which exploits the affine properties of isotropic hypersurfaces (the $\Re$-vacuum). This approach makes it possible to extend the well-known definitions of the vacuum to the case of spaces without symmetries. Relation between this definition and algebraic properties of gravitational field is demonstrated. A possibility of using the notion of the $\Re$-vacuum in studying the problems of localization of the processes of particles creation at quantum evaporization of black holes is pointed out.