  In this paper we show that the one-loop graviton self-energy contribution is
ultraviolet finite, without introducing counterterms, and cutoff-free in the
framework of causal perturbation theory. In addition, it satisfies the
gravitational Slavnov-Ward identities for the two-point connected Green
function. The condition of perturbative gauge invariance to second order for
loop graphs is proved. Corrections to the Newtonian potential are also derived.
