Quantum long-range interactions in general relativity

TL;DR

The paper investigates one-loop quantum corrections to general relativity that generate long-range modifications to the Newton potential and to spin- and velocity-dependent gravitational interactions. Using the background-field method, the authors construct invariant effective operators from vacuum polarization, vertex, and box diagrams, and interpret a subset of these corrections as quantum corrections to the Schwarzschild and Kerr metrics. They demonstrate a universal spin-independent sector and derive explicit expressions for quantum corrections to the Newtonian potential, spin-orbit, and Lense–Thirring interactions, including velocity-dependent terms. The work provides a consistent effective-field-theory framework for quantum gravity corrections at long range, clarifies spin-dependence, and delivers concrete, testable corrections to classical GR predictions.

Abstract

We consider one-loop effects in general relativity which result in quantum long-range corrections to the Newton law, as well as to the gravitational spin-dependent and velocity-dependent interactions. Some contributions to these effects can be interpreted as quantum corrections to the Schwarzschild and Kerr metric.

Figures (4)

• Figure 1: Graviton loop
• Figure 2: Gravitational vertices
• Figure 3: Pole diagrams
• Figure 4: Vertex diagrams