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Abstract: (Springer)
This is a reprinting of a paper by Roger Penrose, first published in a volume of conference proceedings in 1964, no longer easily accessible, in which he first presented the now-standard description of asymptotically flat spacetimes with the help of a conformal mapping, now called a Penrose transform. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Helmut Friedrich.