Abstract
In Minkowski space-time, (locally) space-filling families of null geodesics i.e., null geodesic congruences, appear in a variety different physical contexts. We here describe what appears to be the general explicit generic expression for these congruences. From each congruence one can construct a (virtually) unique form of the flat Lorentzian metric that is associated with the congruence. In addition, the “so-called” optical parameters for each congruence are calculated. The very important special cases of the shear-free congruences (twisting and non-twisting) are described in detail. These results are closely related to the asymptotically shear-free null geodesic congruences of asymptotically flat space-times and their rather surprising physical implications.
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Newman, E.T. Geometry of flat-space null geodesic congruences. Gen Relativ Gravit 52, 69 (2020). https://doi.org/10.1007/s10714-020-02719-6
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DOI: https://doi.org/10.1007/s10714-020-02719-6