Newtonian potential in higher-derivative quantum gravity

TL;DR

This paper derives quantum-corrected Newtonian potentials in higher-derivative gravity, showing improved behavior near the origin but not resolving the singularity, supported by numerical and analytical methods.

Contribution

It provides the first derivation of quantum-corrected Newtonian potentials in fourth-derivative gravity including one-loop effects.

Findings

Quantum corrections modify the Newtonian potential near the origin.

The potential's behavior is improved but still singular at r=0.

Numerical and analytical methods confirm the results.

Abstract

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.