Variations on the Goroff-Sagnotti operator

The Goroff-Sagnotti operator, corresponding to the contraction of three Weyl tensors, is the first counterterm of general relativity (GR) nonvanishing on shell. We study the classical effects of including this operator in the effective gravitational Lagrangian. The results obtained for the Goroff-Sagnotti operator are proved to hold for some higher-curvature operators that generalize it. We find solutions to those operators' equations of motion (EM); in particular, we find the general condition for the spherically symmetric case and provide several example solutions. Concerning the EM for GR supplemented with the Goroff-Sagnotti operator, we study spherically symmetric perturbative corrections to the GR solution. In less symmetric instances, we only study the subset of solutions that solve the EM separately for GR and the Goroff-Sagnotti operator.