EINSTEIN EQUATIONS AND FIERZ-PAULI EQUATIONS WITH SELF-INTERACTION INQUANTUM-GRAVITY

The Einstein equations can be written as Fierz-Pauli equations with se lf-interaction, W gamma(ik) = (ik)+1/2g(ik)g(mn)G(mn)-k(T-ik-1/2g(ik)g (mn)T(mn)) together with the covariant Hilbert-gauge condition, (gamma (i)(h)-1/2 delta(i)(k)g(mn)gamma(mn));(k)=0 where W denotes the couari ant wave operator and G(ik) the Einstein tenser of the metric g(ik) co llecting all nonlinear terms of Einstein's equations. As is known, the re do not, however, exist plane-wave solutions gamma(ik)(Z) with g(ik) Z(,i)Z(,k) = 0 of these equations such that what is essential to the i ntroduction of gravitons is not satisfied in general relativity. This nonexistence corresponds with the uncertainty relation, Delta p (Delta g)(2) (Delta x)(3) greater than or equal to h hG/c(3) concerning the total nonlinear gravitational field g(ik) = g(ik) + gamma(ik).