The fluid-ray tetrad formulation of Einstein's field equations

The authors describe the fluid-ray (FR) tetrad, which is based on the four-velocity u of the cosmological fluid and the null vector k which lies along the generators of the null geodesics in the past light cones C ^-(p₀) centred on the worldline C. Then, they formulate the field equations in terms of this tetrad, giving also the Jacobi identities, the metric variable equations for observational coordinates, and the contracted Bianchi identities. The equivalent set of equations, involving the Ricci identities, the full Bianchi identities, along with the contracted Bianchi identities, is also given. This formulation facilitates the integration of the field equations in certain cosmological contexts.