Abstract
In a space-time M, a conformal structure is defined by the distribution of light-cones. Geodesics are traced by freely falling particles, and the collection of all unparameterized geodesics determines the projective structure of M. The article contains a formulation of the necessary and sufficient conditions for these structures to be compatible, i.e. to come from a metric tensor which is then unique up to a constant factor. The theorem applies to all dimensions and signatures.
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Communicated by P. T. Chruściel
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Matveev, V.S., Trautman, A. A Criterion for Compatibility of Conformal and Projective Structures. Commun. Math. Phys. 329, 821–825 (2014). https://doi.org/10.1007/s00220-013-1850-7
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DOI: https://doi.org/10.1007/s00220-013-1850-7