Asymptotic behaviours of 1-loop vertices in the gravitational effective action

The vacuum corrections to the Lagrangian of gravity theory are calculated in the one-loop approximation to third order in the curvature. In the spacetime domain near null infinity the loop expansion of field theory gives the correct results. The small- behaviours of the form factors in the effective action determine the vacuum radiation by the gravitational collapse. These behaviours are presented below and they contain unexpected terms which apparently violate the asymptotic flatness. These terms should ultimately cancel to give the finite flux of vacuum energy.