Republication of: The geometry of free fall and light propagation


This is a reprinting of the paper by Jürgen Ehlers, Felix Pirani and Alfred Schild, first published in 1972 in a separate volume containing articles written in hounour of J. L. Synge. The original book is long out of print and almost forgotten by today. The authors present a method of deriving the Lorentzian geometry from compatible conformal and projective structures on a four dimensional manifold. 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 Andrzej Trautman.

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Correspondence to Felix A. E. Pirani.

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An editorial note to this paper can be found in this issue preceding this Golden Oldie and online via doi:10.1007/s10714-012-1352-5.

Original paper: J. Ehlers, F. A. E. Pirani and A. Schild, in: General Relativity, papers in honour of J. L. Synge. Edited by L. O’Reifeartaigh. Oxford, Clarendon Press 1972, pp. 63–84. Reprinted with the kind permissions of Felix A. E. Pirani, of the Oxford University Press and of the Royal Irish Academy.

J. Ehlers (Deceased May 20, 2008)

A. Schild (Deceased May 24, 1977)

Editorial responsibility: A. Krasiński, e-mail:

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Ehlers, J., Pirani, F.A.E. & Schild, A. Republication of: The geometry of free fall and light propagation. Gen Relativ Gravit 44, 1587–1609 (2012).

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  • Manifold
  • General Relativity
  • Differential Geometry
  • Light Propagation
  • Dimensional Manifold