Geodesic
Klein-Gordon equation in Riemannian space
Teoretičeskaâ i matematičeskaâ fizika, Tome 13 (1972) no. 1, pp. 140-142 Cet article a éte moissonné depuis la source Math-Net.Ru

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A solution that depends on $a(t)$ is obtained for the Klein–Gordon equation in the metric of a closed Fridman model. The metric's being non-Euclidean and time-dependent leads to the wave function's being damped in the f i r s t order and the frequency's being reduced in the second order of an expansion in the small parameter $H/\omega_0\sim10^{-40}$. 
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     author = {A. P. Bondarev and K. P. Stanyukovich},
     title = {Klein-Gordon equation in {Riemannian} space},
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     year = {1972},
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}
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A. P. Bondarev; K. P. Stanyukovich. Klein-Gordon equation in Riemannian space. Teoretičeskaâ i matematičeskaâ fizika, Tome 13 (1972) no. 1, pp. 140-142. http://geodesic.mathdoc.fr/item/TMF_1972_13_1_a11/

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[3] K. P. Stanyukovich, Gravitatsionnoe pole i elementarnye chastitsy, «Nauka», 1965 | MR | Zbl