Exact Nonnull Wavelike Solutions to Gravity with Quadratic Lagrangians

Abstract

Solutions to gravity with quadratic Lagrangians are found for the simple case where the only nonconstant metric component is the lapse $N$ and the Riemann tensor takes the form $R^{t}_{.itj}=-k_{i}k_{j}, i,j=1,2,3$; thus these solutions depend on cross terms in the Riemann tensor and therefore complement the linearized theory where it is the derivatives of the Riemann tensor that matter. The relationship of this metric to the null gravitational radiation metric of Peres is given. Gravitaional energy Poynting vectors are construcetd for the solutions and one of these, based on the Lanczos tensor, supports the indication in the linearized theory that nonnull gravitational radiation can occur.