The one-loop form factors in the effective action, and production of coherent gravitons from the vacuum

We present the solution of the problem of the \(1/\Box, \Box \to 0,\) asymptotic terms discovered in the one-loop form factors of the gravitational effective action. Owing to certain constraints among their coefficients, which we establish, these terms cancel in the vacuum stress tensor and do not violate the asymptotic flatness of the expectation value of the metric. They reappear, however, in the Riemann tensor of this metric and stand for a new effect: a radiation of gravitational waves induced by the vacuum stress. This coherent radiation caused by the backreaction adds to the noncoherent radiation caused by the pair creation in the case where the initial state provides the vacuum stress tensor with a quadrupole moment.