SL(2, C) Symmetry of the Gravitational Field Dynamical Variables

Abstract

We represent the spin coefficients and the Riemann tensor in the form of linear combinations of the infinitesimal generators of the group SL(2, C). This representation is similar to the way Yang and Mills write their dynamical variables in terms of the Pauli spin matrices. The spin coefficients take the role of the Yang‐Mills‐like potentials, whereas the Riemann tensor takes the role of the fields.