Newtonian potential in higher-derivative quantum gravity

We hereby derive the Newtonian metric potentials for the fourth-derivative gravity including the one-loop logarithm quantum corrections. It is explicitly shown that the behavior of the modified Newtonian potential near the origin is improved respect to the classical one, but this is not enough to remove the curvature singularity in r = 0. Our result is grounded on a rigorous proof based on numerical and analytic computations.

Automated summary

The Newtonian metric potentials for fourth-derivative gravity with one-loop logarithm quantum corrections were derived. The modified Newtonian potential near the origin was shown to be improved compared to the classical one, but the curvature singularity at r = 0 remains. The results are based on a rigorous proof involving numerical and analytic computations.