Uniqueness of the metric from the Weyl and energy-momentum tensors
Graham S. Hall, Alan D. Rendall · Journal of Mathematical Physics · 1987
It is shown that for a general space-time in Einstein’s theory (with the term ‘‘general’’ being precisely defined) the Weyl tensor and energy-momentum tensor determine the metric up to a constant conformal factor. One of the conclusions may be interpreted as a generalization of the well-known Brinkmann theorem characterizing pp waves in vacuo.