Geodesic
On the definition of the vacuum in the Gravitational field; the $\Re$ vacuum
Teoretičeskaâ i matematičeskaâ fizika, Tome 33 (1977) no. 1, pp. 3-16

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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. 
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     title = {On the definition of the vacuum in the {Gravitational} field; the $\Re$ vacuum},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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I. V. Volovich; V. A. Zagrebnov; V. P. Frolov. On the definition of the vacuum in the Gravitational field; the $\Re$ vacuum. Teoretičeskaâ i matematičeskaâ fizika, Tome 33 (1977) no. 1, pp. 3-16. http://geodesic.mathdoc.fr/item/TMF_1977_33_1_a0/