Trace anomaly, effective approach, and gravitational potential

Abstract

We explore and discuss corrections to the Newton potential from the quantum effects of conformal matter fields. In this special case, one can compare different approaches, including that of effective quantum gravity and another, based on the conformal (trace) anomaly. The comparison of these two methods is the main focus in the present work. Using the anomaly-induced effective action of gravity requires fixing the quantum vacuum state, similar to what is done in the description of black hole evaporation. In the Boulware vacuum state, we compute the anomaly-induced stress tensor and the first-order correction to the classical gravitational law. The quantum correction to the Newton's potential derived in this way, differs from the result calculated in a way analogous to the effective approach to quantum gravity. The only way to reconcile the two approaches for deriving the leading semiclassical corrections to Newtonian potential is to modify the asymptotic behavior of the average of the energy-momentum tensor in the Boulware vacuum state, as has been recently discussed in the literature.