The author considers the Klein-Gordon equation for -dimensional flat spacetime. He is interested in those coordinate systems for which the equation is separable. These coordinate systems are explicitly known and generally do not cover the whole plane. The author constructs tensor fields which he can use to express the locus of points where the coordinates break down.
@article{701599,
title = {Local and global aspects of separating coordinates for the Klein-Gordon equation},
booktitle = {Proceedings of the 16th Winter School "Geometry and Physics"},
series = {GDML\_Books},
publisher = {Circolo Matematico di Palermo},
address = {Palermo},
year = {1997},
pages = {[97]-105},
mrnumber = {MR1469025},
zbl = {0879.53061},
url = {http://dml.mathdoc.fr/item/701599}
}
Hinterleitner, Franz. Local and global aspects of separating coordinates for the Klein-Gordon equation, dans Proceedings of the 16th Winter School "Geometry and Physics", GDML_Books, (1997), pp. [97]-105. http://gdmltest.u-ga.fr/item/701599/