Topology change without any pathology (Q1893825)

The author constructs examples of spherically symmetric spacetimes without causality violation or singularities but with topology change. This is not in contradiction to theorems by \textit{R. P. Geroch} [J. Math. Phys. 8, 782-786 (1967; Zbl 0158.465)] and \textit{F. J. Tipler} [Ann. Phys. 108, 1-36 (1977; Zbl 0369.53057)] since in Krasnikov's construction the topology change takes place at infinity. He or she considers spacetimes with the metric \(g = -f^{-2} (\alpha, \beta) d \alpha d\beta + R^2 (\sin^2 (\vartheta) d \varphi^2 + d\vartheta^2)\) (\(R\) seems really to be constant). Generically, those points corresponding to \(f = 0\) are at infinity and by choosing \(f\) adequately, it is possible to enforce topology change at some of these points.