EXACT NONNULL WAVE-LIKE SOLUTIONS TO GRAVITY WITH QUADRATIC LAGRANGIANS

Solutions to gravity with quadratic Lagrangians are found for the simp le case where the only nonconstant metric component is the lapse N and the Riemann tenser takes the form R(itj)(t) = -k(i)k(j), i, j = 1,2,3 ; thus these solutions depend on cross terms in the Riemann tensor and therefore complement linearized theory where it is the derivatives of the Riemann tenser that matter. The relationship of this metric to th e null gravitational radiation metric of Peres is given. Gravitational energy Poynting vectors are constructed for the solutions and one of these, based on the Lanczos tenser, supports the indication in the lin earized theory that nonnull gravitational radiation can occur.