The Determination of the Metric by the Weyl and Energy-Momentum Tensors
  This brief paper investigates the consequences for the metric tensor of space-time when the Weyl tensor (in its conformally invariant form) and the energy-momentum tensor is specified. It is shown that, unless rather special conditions hold, the metric is uniquely determined up to a constant conformal factor. 
G.S. Hall and M. Sharif