Twistor-gauge interpretation of Einstein-Hilbert equations (Q1103893)

The author considers the twistor interpretation of the pure Einstein equations \((J=0)\) based on the following description due to D. Popov and L. Dajkhin: For any energy-momentum tensor \(T_{ij}\) there exists a current J such that the Einstein equations \(R_{ij}-()g_{ij}R=\chi T_{ij}\) are equivalent to the equations: \(\Delta R=J\), where R is the Cartan curvature on a pseudo-Riemannian four-dimensional manifold.