Geodesic
Plane waves, Batmen's solutions and sources at infinity
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 44, Tome 426 (2014), pp. 23-33

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For threedimensional wave equation two equivalent statements are proved: 1) plane waves are not generated by a source at infinity, 2) Bateman's solution (the solution that obtained by the application of Kelvin–Bateman transformation to a plane wave) is the solution to wave equation everywhere in $\mathbb R^4$. 
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     author = {A. S. Blagovestchensky},
     title = {Plane waves, {Batmen's} solutions and sources at infinity},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {23--33},
     publisher = {mathdoc},
     volume = {426},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_426_a3/}
}
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A. S. Blagovestchensky. Plane waves, Batmen's solutions and sources at infinity. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 44, Tome 426 (2014), pp. 23-33. http://geodesic.mathdoc.fr/item/ZNSL_2014_426_a3/