Spherically-symmetric solutions with a chain of n internal Ricci-flat spaces

Abstract

The Schwarzschild solution is generalized for the case of n internal Ricci-flat spaces. It is shown that in the four-dimensional section of the metric a horizon exists only when the internal space scale factors are constant. The scalar-vacuum generalization of the solution is also presented. [This paper is the English translation of the part of Chapter. 2.4 of the author's PhD dissertation (Moscow, 1989).]